Space of modular forms of level 7440, weight 2, and trivial character

• Label: 7440.2.a
• Level: $7440$
• Weight: $2$
• Character orbit: 7440.a
• Rep. character: $\chi_{7440}(1,\cdot)$
• Character field: $\Q$
• Dimension: $120$
• Newform subspaces: $58$
• Sturm bound: $3072$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 7440 = 2^{4} \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7440.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 58 \)
Sturm bound:			\(3072\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7440))\).

	Total	New	Old
Modular forms	1560	120	1440
Cusp forms	1513	120	1393
Eisenstein series	47	0	47

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	\(5\)	\(31\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(7\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(8\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(9\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(6\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(8\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(7\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(6\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(9\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(8\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(7\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(6\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(9\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(7\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(8\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(9\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(6\)
Plus space				\(+\)	\(52\)
Minus space				\(-\)	\(68\)

Trace form

120 * q - 8 * q^7 + 120 * q^9 - 16 * q^11 - 16 * q^23 + 120 * q^25 + 32 * q^29 + 32 * q^37 - 16 * q^41 - 16 * q^43 + 104 * q^49 + 32 * q^53 - 8 * q^63 - 16 * q^65 + 8 * q^67 + 32 * q^71 + 32 * q^77 - 16 * q^79 + 120 * q^81 + 48 * q^83 - 24 * q^87 - 16 * q^89 - 48 * q^91 - 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7440))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	5	31
7440.2.a.a	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				930.2.a.g	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-4\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
7440.2.a.b	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				930.2.a.n	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{7}+q^{9}-4q^{13}+q^{15}+\cdots\)
7440.2.a.c	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				930.2.a.f	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}-5q^{11}+2q^{13}+\cdots\)
7440.2.a.d	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				3720.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}-2q^{13}+q^{15}-2q^{17}+\cdots\)
7440.2.a.e	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				3720.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+2q^{7}+q^{9}+q^{15}+2q^{17}+\cdots\)
7440.2.a.f	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				3720.2.a.h	$1$	$2$	\(0\)	\(-1\)	\(1\)	\(-4\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-4q^{7}+q^{9}-6q^{11}-6q^{13}+\cdots\)
7440.2.a.g	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				930.2.a.j	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-4\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-4q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
7440.2.a.h	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				1860.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots\)
7440.2.a.i	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				3720.2.a.g	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}-2q^{13}-q^{15}+6q^{17}+\cdots\)
7440.2.a.j	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				930.2.a.o	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\)
7440.2.a.k	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				930.2.a.i	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+3q^{11}+2q^{13}+\cdots\)
7440.2.a.l	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				1860.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots\)
7440.2.a.m	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				930.2.a.h	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots\)
7440.2.a.n	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				3720.2.a.f	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(3\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+3q^{7}+q^{9}-3q^{11}-2q^{13}+\cdots\)
7440.2.a.o	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				465.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(4\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
7440.2.a.p	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				930.2.a.m	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-3q^{7}+q^{9}-5q^{11}-6q^{13}+\cdots\)
7440.2.a.q	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				930.2.a.b	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\)
7440.2.a.r	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				930.2.a.l	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+6q^{11}-2q^{13}+\cdots\)
7440.2.a.s	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				3720.2.a.b	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}+3q^{11}-6q^{13}+\cdots\)
7440.2.a.t	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				3720.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}+q^{9}+4q^{13}-q^{15}+\cdots\)
7440.2.a.u	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				930.2.a.k	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}+q^{9}+4q^{13}-q^{15}+\cdots\)
7440.2.a.v	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				930.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(3\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+3q^{7}+q^{9}-3q^{11}-2q^{13}+\cdots\)
7440.2.a.w	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				3720.2.a.c	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-4\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-4q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
7440.2.a.x	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				930.2.a.e	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-3\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-3q^{7}+q^{9}-3q^{11}-2q^{13}+\cdots\)
7440.2.a.y	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				930.2.a.d	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots\)
7440.2.a.z	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				1860.2.a.a	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}-2q^{13}+q^{15}-4q^{17}+\cdots\)
7440.2.a.ba	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				465.2.a.b	$1$	$0$	\(0\)	\(1\)	\(1\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+2q^{7}+q^{9}+4q^{11}+q^{15}+\cdots\)
7440.2.a.bb	$7440$	$2$	7440.a	1.a	$1$	$1$	$1$	$59.409$	\(\Q\)	None	✓				930.2.a.c	$1$	$0$	\(0\)	\(1\)	\(1\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+4q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
7440.2.a.bc	$7440$	$2$	7440.a	1.a	$1$	$2$	$2$	$59.409$	\(\Q(\sqrt{3}) \)	None	✓				1860.2.a.e	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(-1+\beta )q^{7}+q^{9}+4q^{11}+\cdots\)
7440.2.a.bd	$7440$	$2$	7440.a	1.a	$1$	$2$	$2$	$59.409$	\(\Q(\sqrt{65}) \)	None	✓				930.2.a.q	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
7440.2.a.be	$7440$	$2$	7440.a	1.a	$1$	$2$	$2$	$59.409$	\(\Q(\sqrt{2}) \)	None	✓				465.2.a.c	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(2+\beta )q^{7}+q^{9}-2\beta q^{11}+\cdots\)
7440.2.a.bf	$7440$	$2$	7440.a	1.a	$1$	$2$	$2$	$59.409$	\(\Q(\sqrt{3}) \)	None	✓				3720.2.a.k	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-6\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(-3+\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
7440.2.a.bg	$7440$	$2$	7440.a	1.a	$1$	$2$	$2$	$59.409$	\(\Q(\sqrt{33}) \)	None	✓				930.2.a.r	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(-1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-\beta q^{7}+q^{9}+(-4+\beta )q^{11}+\cdots\)
7440.2.a.bh	$7440$	$2$	7440.a	1.a	$1$	$2$	$2$	$59.409$	\(\Q(\sqrt{2}) \)	None	✓				3720.2.a.j	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(4\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(2+\beta )q^{7}+q^{9}-2\beta q^{11}+\cdots\)
7440.2.a.bi	$7440$	$2$	7440.a	1.a	$1$	$2$	$2$	$59.409$	\(\Q(\sqrt{5}) \)	None	✓				3720.2.a.i	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(-1-\beta )q^{7}+q^{9}+(-1+\cdots)q^{13}+\cdots\)
7440.2.a.bj	$7440$	$2$	7440.a	1.a	$1$	$2$	$2$	$59.409$	\(\Q(\sqrt{6}) \)	None	✓				1860.2.a.d	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+\beta q^{7}+q^{9}+(-2+\beta )q^{13}+\cdots\)
7440.2.a.bk	$7440$	$2$	7440.a	1.a	$1$	$2$	$2$	$59.409$	\(\Q(\sqrt{3}) \)	None	✓				465.2.a.d	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(6\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(3+\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
7440.2.a.bl	$7440$	$2$	7440.a	1.a	$1$	$2$	$2$	$59.409$	\(\Q(\sqrt{17}) \)	None	✓				930.2.a.p	$1$	$0$	\(0\)	\(2\)	\(2\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-\beta q^{7}+q^{9}-\beta q^{11}+2q^{13}+\cdots\)
7440.2.a.bm	$7440$	$2$	7440.a	1.a	$1$	$3$	$3$	$59.409$	3.3.148.1	None	✓		✓		465.2.a.g	$1$	$1$	\(0\)	\(-3\)	\(-3\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(-2\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
7440.2.a.bn	$7440$	$2$	7440.a	1.a	$1$	$3$	$3$	$59.409$	3.3.404.1	None	✓		✓		1860.2.a.g	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(1-\beta _{2})q^{7}+q^{9}-2\beta _{2}q^{11}+\cdots\)
7440.2.a.bo	$7440$	$2$	7440.a	1.a	$1$	$3$	$3$	$59.409$	3.3.148.1	None	✓				3720.2.a.o	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(2\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(1-\beta _{1})q^{7}+q^{9}+(2\beta _{1}+\cdots)q^{11}+\cdots\)
7440.2.a.bp	$7440$	$2$	7440.a	1.a	$1$	$3$	$3$	$59.409$	3.3.148.1	None	✓		✓		465.2.a.f	$1$	$1$	\(0\)	\(-3\)	\(3\)	\(-2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(-1+\beta _{1})q^{7}+q^{9}-2q^{11}+\cdots\)
7440.2.a.bq	$7440$	$2$	7440.a	1.a	$1$	$3$	$3$	$59.409$	3.3.7636.1	None	✓		✓		1860.2.a.h	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+\beta _{1}q^{7}+q^{9}-2q^{11}+\cdots\)
7440.2.a.br	$7440$	$2$	7440.a	1.a	$1$	$3$	$3$	$59.409$	3.3.148.1	None	✓				3720.2.a.p	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(2\beta _{1}+\beta _{2})q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
7440.2.a.bs	$7440$	$2$	7440.a	1.a	$1$	$3$	$3$	$59.409$	3.3.564.1	None	✓		✓		465.2.a.e	$1$	$1$	\(0\)	\(3\)	\(-3\)	\(-8\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(-3+\beta _{1})q^{7}+q^{9}-2\beta _{1}q^{11}+\cdots\)
7440.2.a.bt	$7440$	$2$	7440.a	1.a	$1$	$3$	$3$	$59.409$	3.3.564.1	None	✓		✓		1860.2.a.f	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(-4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
7440.2.a.bu	$7440$	$2$	7440.a	1.a	$1$	$3$	$3$	$59.409$	3.3.404.1	None	✓		✓		3720.2.a.l	$1$	$1$	\(0\)	\(3\)	\(-3\)	\(2\)		$+$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(1+\beta _{1})q^{7}+q^{9}-4q^{11}+\cdots\)
7440.2.a.bv	$7440$	$2$	7440.a	1.a	$1$	$3$	$3$	$59.409$	3.3.316.1	None	✓				3720.2.a.n	$1$	$1$	\(0\)	\(3\)	\(3\)	\(-2\)		$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(-1-\beta _{2})q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
7440.2.a.bw	$7440$	$2$	7440.a	1.a	$1$	$3$	$3$	$59.409$	3.3.568.1	None	✓				3720.2.a.m	$1$	$1$	\(0\)	\(3\)	\(3\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-\beta _{1}q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots\)
7440.2.a.bx	$7440$	$2$	7440.a	1.a	$1$	$4$	$4$	$59.409$	4.4.78292.1	None	✓				3720.2.a.r	$1$	$0$	\(0\)	\(4\)	\(-4\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-\beta _{1}q^{7}+q^{9}+(-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
7440.2.a.by	$7440$	$2$	7440.a	1.a	$1$	$4$	$4$	$59.409$	4.4.70164.1	None	✓				3720.2.a.q	$1$	$0$	\(0\)	\(4\)	\(-4\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+\beta _{3}q^{7}+q^{9}+2q^{11}+\cdots\)
7440.2.a.bz	$7440$	$2$	7440.a	1.a	$1$	$4$	$4$	$59.409$	4.4.8468.1	None	✓		✓		465.2.a.h	$1$	$1$	\(0\)	\(4\)	\(4\)	\(-4\)		$-$	$-$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(-1+\beta _{1}-\beta _{3})q^{7}+q^{9}+\cdots\)
7440.2.a.ca	$7440$	$2$	7440.a	1.a	$1$	$4$	$4$	$59.409$	4.4.92692.1	None	✓				3720.2.a.t	$1$	$0$	\(0\)	\(4\)	\(4\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+\beta _{2}q^{7}+q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
7440.2.a.cb	$7440$	$2$	7440.a	1.a	$1$	$4$	$4$	$59.409$	4.4.224148.1	None	✓		✓		1860.2.a.i	$1$	$0$	\(0\)	\(4\)	\(4\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(1-\beta _{1})q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
7440.2.a.cc	$7440$	$2$	7440.a	1.a	$1$	$4$	$4$	$59.409$	4.4.17428.1	None	✓				3720.2.a.s	$1$	$0$	\(0\)	\(4\)	\(4\)	\(4\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(1-\beta _{3})q^{7}+q^{9}+(2-\beta _{1}+\cdots)q^{11}+\cdots\)
7440.2.a.cd	$7440$	$2$	7440.a	1.a	$1$	$5$	$5$	$59.409$	5.5.2294036.1	None	✓		✓		3720.2.a.v	$1$	$1$	\(0\)	\(-5\)	\(-5\)	\(-3\)		$+$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(-1+\beta _{2})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
7440.2.a.ce	$7440$	$2$	7440.a	1.a	$1$	$5$	$5$	$59.409$	5.5.5547956.1	None	✓		✓		3720.2.a.u	$1$	$0$	\(0\)	\(-5\)	\(-5\)	\(1\)		$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(\beta _{1}+\beta _{3})q^{7}+q^{9}+(\beta _{3}+\cdots)q^{11}+\cdots\)
7440.2.a.cf	$7440$	$2$	7440.a	1.a	$1$	$5$	$5$	$59.409$	5.5.24504404.1	None	✓		✓		3720.2.a.w	$1$	$0$	\(0\)	\(-5\)	\(5\)	\(-1\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-\beta _{1}q^{7}+q^{9}+\beta _{4}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7440))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7440)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(124))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(186))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(248))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(310))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(372))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(465))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(496))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(620))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(744))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(930))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1488))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1860))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2480))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3720))\)\(^{\oplus 2}\)