Space of modular forms of level 7448, weight 2, and trivial character

• Label: 7448.2.a
• Level: $7448$
• Weight: $2$
• Character orbit: 7448.a
• Rep. character: $\chi_{7448}(1,\cdot)$
• Character field: $\Q$
• Dimension: $185$
• Newform subspaces: $50$
• Sturm bound: $2240$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 7448 = 2^{3} \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7448.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 50 \)
Sturm bound:			\(2240\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7448))\).

	Total	New	Old
Modular forms	1152	185	967
Cusp forms	1089	185	904
Eisenstein series	63	0	63

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

\(2\)	\(7\)	\(19\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(136\)	\(23\)	\(113\)		\(129\)	\(23\)	\(106\)		\(7\)	\(0\)	\(7\)
\(+\)	\(+\)	\(-\)	\(-\)		\(148\)	\(23\)	\(125\)		\(140\)	\(23\)	\(117\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(+\)	\(-\)		\(149\)	\(23\)	\(126\)		\(141\)	\(23\)	\(118\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(-\)	\(+\)		\(143\)	\(23\)	\(120\)		\(135\)	\(23\)	\(112\)		\(8\)	\(0\)	\(8\)
\(-\)	\(+\)	\(+\)	\(-\)		\(152\)	\(26\)	\(126\)		\(144\)	\(26\)	\(118\)		\(8\)	\(0\)	\(8\)
\(-\)	\(+\)	\(-\)	\(+\)		\(140\)	\(20\)	\(120\)		\(132\)	\(20\)	\(112\)		\(8\)	\(0\)	\(8\)
\(-\)	\(-\)	\(+\)	\(+\)		\(139\)	\(19\)	\(120\)		\(131\)	\(19\)	\(112\)		\(8\)	\(0\)	\(8\)
\(-\)	\(-\)	\(-\)	\(-\)		\(145\)	\(28\)	\(117\)		\(137\)	\(28\)	\(109\)		\(8\)	\(0\)	\(8\)
Plus space			\(+\)		\(558\)	\(85\)	\(473\)		\(527\)	\(85\)	\(442\)		\(31\)	\(0\)	\(31\)
Minus space			\(-\)		\(594\)	\(100\)	\(494\)		\(562\)	\(100\)	\(462\)		\(32\)	\(0\)	\(32\)

Trace form

185 * q - 4 * q^5 + 183 * q^9 - 6 * q^11 + 2 * q^13 - 16 * q^15 - 6 * q^17 + 3 * q^19 + 6 * q^23 + 201 * q^25 - 24 * q^27 + 14 * q^29 + 4 * q^31 + 4 * q^33 - 14 * q^37 + 26 * q^39 - 2 * q^41 - 14 * q^43 - 16 * q^45 - 30 * q^47 + 4 * q^51 + 10 * q^53 - 6 * q^55 + 2 * q^57 - 8 * q^59 - 24 * q^61 + 16 * q^65 - 20 * q^67 + 20 * q^69 + 8 * q^71 + 14 * q^73 - 20 * q^75 - 20 * q^79 + 169 * q^81 + 40 * q^83 + 42 * q^85 + 10 * q^87 + 14 * q^89 + 4 * q^93 + 22 * q^97 + 62 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7448))\) 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	7	19
7448.2.a.a	$7448$	$2$	7448.a	1.a	$1$	$1$	$1$	$59.473$	\(\Q\)	None	✓				1064.2.q.a	$1$	$2$	\(0\)	\(-2\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+q^{9}-3q^{11}-4q^{13}+\cdots\)
7448.2.a.b	$7448$	$2$	7448.a	1.a	$1$	$1$	$1$	$59.473$	\(\Q\)	None	✓				1064.2.q.i	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+q^{9}-q^{11}+2q^{13}+\cdots\)
7448.2.a.c	$7448$	$2$	7448.a	1.a	$1$	$1$	$1$	$59.473$	\(\Q\)	None	✓				1064.2.q.j	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
7448.2.a.d	$7448$	$2$	7448.a	1.a	$1$	$1$	$1$	$59.473$	\(\Q\)	None	✓				1064.2.q.c	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+q^{9}-3q^{11}-6q^{13}+\cdots\)
7448.2.a.e	$7448$	$2$	7448.a	1.a	$1$	$1$	$1$	$59.473$	\(\Q\)	None	✓				1064.2.q.b	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+q^{9}+3q^{11}+2q^{13}+\cdots\)
7448.2.a.f	$7448$	$2$	7448.a	1.a	$1$	$1$	$1$	$59.473$	\(\Q\)	None	✓				1064.2.q.h	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+2q^{5}+q^{9}-q^{11}-4q^{13}+\cdots\)
7448.2.a.g	$7448$	$2$	7448.a	1.a	$1$	$1$	$1$	$59.473$	\(\Q\)	None	✓				152.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{9}+2q^{11}-q^{13}+5q^{17}+\cdots\)
7448.2.a.h	$7448$	$2$	7448.a	1.a	$1$	$1$	$1$	$59.473$	\(\Q\)	None	✓				1064.2.q.d	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-3q^{9}-q^{11}+6q^{17}+q^{19}+\cdots\)
7448.2.a.i	$7448$	$2$	7448.a	1.a	$1$	$1$	$1$	$59.473$	\(\Q\)	None	✓				1064.2.q.g	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-3q^{9}-q^{11}+2q^{13}+2q^{17}+\cdots\)
7448.2.a.j	$7448$	$2$	7448.a	1.a	$1$	$1$	$1$	$59.473$	\(\Q\)	None	✓				1064.2.q.e	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-3q^{9}+5q^{11}+4q^{13}-2q^{17}+\cdots\)
7448.2.a.k	$7448$	$2$	7448.a	1.a	$1$	$1$	$1$	$59.473$	\(\Q\)	None	✓				1064.2.q.f	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-3q^{9}-q^{11}-2q^{13}+3q^{17}+\cdots\)
7448.2.a.l	$7448$	$2$	7448.a	1.a	$1$	$1$	$1$	$59.473$	\(\Q\)	None	✓				1064.2.q.f	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-3q^{9}-q^{11}+2q^{13}-3q^{17}+\cdots\)
7448.2.a.m	$7448$	$2$	7448.a	1.a	$1$	$1$	$1$	$59.473$	\(\Q\)	None	✓				1064.2.q.g	$1$	$1$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-3q^{9}-q^{11}-2q^{13}-2q^{17}+\cdots\)
7448.2.a.n	$7448$	$2$	7448.a	1.a	$1$	$1$	$1$	$59.473$	\(\Q\)	None	✓				1064.2.q.d	$1$	$1$	\(0\)	\(0\)	\(3\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-3q^{9}-q^{11}-6q^{17}-q^{19}+\cdots\)
7448.2.a.o	$7448$	$2$	7448.a	1.a	$1$	$1$	$1$	$59.473$	\(\Q\)	None	✓				1064.2.q.e	$1$	$1$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-3q^{9}+5q^{11}-4q^{13}+2q^{17}+\cdots\)
7448.2.a.p	$7448$	$2$	7448.a	1.a	$1$	$1$	$1$	$59.473$	\(\Q\)	None	✓				1064.2.q.h	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{5}+q^{9}-q^{11}+4q^{13}+\cdots\)
7448.2.a.q	$7448$	$2$	7448.a	1.a	$1$	$1$	$1$	$59.473$	\(\Q\)	None	✓				1064.2.q.c	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+q^{9}-3q^{11}+6q^{13}+\cdots\)
7448.2.a.r	$7448$	$2$	7448.a	1.a	$1$	$1$	$1$	$59.473$	\(\Q\)	None	✓				1064.2.q.b	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+q^{9}+3q^{11}-2q^{13}+\cdots\)
7448.2.a.s	$7448$	$2$	7448.a	1.a	$1$	$1$	$1$	$59.473$	\(\Q\)	None	✓				152.2.a.a	$1$	$1$	\(0\)	\(2\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+q^{9}-3q^{11}+4q^{13}+\cdots\)
7448.2.a.t	$7448$	$2$	7448.a	1.a	$1$	$1$	$1$	$59.473$	\(\Q\)	None	✓				1064.2.q.a	$1$	$0$	\(0\)	\(2\)	\(1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+q^{9}-3q^{11}+4q^{13}+\cdots\)
7448.2.a.u	$7448$	$2$	7448.a	1.a	$1$	$1$	$1$	$59.473$	\(\Q\)	None	✓				1064.2.q.i	$1$	$1$	\(0\)	\(2\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+q^{9}-q^{11}-2q^{13}+\cdots\)
7448.2.a.v	$7448$	$2$	7448.a	1.a	$1$	$1$	$1$	$59.473$	\(\Q\)	None	✓				1064.2.q.j	$1$	$0$	\(0\)	\(2\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
7448.2.a.w	$7448$	$2$	7448.a	1.a	$1$	$2$	$2$	$59.473$	\(\Q(\sqrt{57}) \)	None	✓				1064.2.q.l	$1$	$1$	\(0\)	\(-4\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+q^{9}+(-1-\beta )q^{11}+\cdots\)
7448.2.a.x	$7448$	$2$	7448.a	1.a	$1$	$2$	$2$	$59.473$	\(\Q(\sqrt{2}) \)	None	✓				1064.2.q.k	$1$	$1$	\(0\)	\(-4\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{3}+q^{5}+(3-4\beta )q^{9}+(1+\cdots)q^{11}+\cdots\)
7448.2.a.y	$7448$	$2$	7448.a	1.a	$1$	$2$	$2$	$59.473$	\(\Q(\sqrt{5}) \)	None	✓				1064.2.a.e	$1$	$1$	\(0\)	\(-3\)	\(-5\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(-2-\beta )q^{5}+(-1+\cdots)q^{9}+\cdots\)
7448.2.a.z	$7448$	$2$	7448.a	1.a	$1$	$2$	$2$	$59.473$	\(\Q(\sqrt{5}) \)	None	✓				1064.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}+(-2+\beta )q^{9}+(1-3\beta )q^{11}+\cdots\)
7448.2.a.ba	$7448$	$2$	7448.a	1.a	$1$	$2$	$2$	$59.473$	\(\Q(\sqrt{5}) \)	None	✓				1064.2.a.c	$1$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1-2\beta )q^{5}+(-2+\beta )q^{9}+\cdots\)
7448.2.a.bb	$7448$	$2$	7448.a	1.a	$1$	$2$	$2$	$59.473$	\(\Q(\sqrt{13}) \)	None	✓				1064.2.a.b	$1$	$1$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}+\beta q^{9}+(-1+\beta )q^{11}+\cdots\)
7448.2.a.bc	$7448$	$2$	7448.a	1.a	$1$	$2$	$2$	$59.473$	\(\Q(\sqrt{5}) \)	None	✓				1064.2.a.a	$1$	$0$	\(0\)	\(3\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(-1+2\beta )q^{5}+(-1+3\beta )q^{9}+\cdots\)
7448.2.a.bd	$7448$	$2$	7448.a	1.a	$1$	$2$	$2$	$59.473$	\(\Q(\sqrt{2}) \)	None	✓				1064.2.q.k	$1$	$1$	\(0\)	\(4\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{3}-q^{5}+(3+4\beta )q^{9}+(1-3\beta )q^{11}+\cdots\)
7448.2.a.be	$7448$	$2$	7448.a	1.a	$1$	$2$	$2$	$59.473$	\(\Q(\sqrt{57}) \)	None	✓				1064.2.q.l	$1$	$1$	\(0\)	\(4\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+q^{9}+(-2+\beta )q^{11}+\cdots\)
7448.2.a.bf	$7448$	$2$	7448.a	1.a	$1$	$3$	$3$	$59.473$	3.3.961.1	None	✓				152.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{2}q^{5}+(5-\beta _{1}+2\beta _{2})q^{9}+\cdots\)
7448.2.a.bg	$7448$	$2$	7448.a	1.a	$1$	$3$	$3$	$59.473$	3.3.1076.1	None	✓				1064.2.q.m	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
7448.2.a.bh	$7448$	$2$	7448.a	1.a	$1$	$3$	$3$	$59.473$	3.3.1076.1	None	✓				1064.2.q.m	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2})q^{5}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
7448.2.a.bi	$7448$	$2$	7448.a	1.a	$1$	$3$	$3$	$59.473$	3.3.1101.1	None	✓				1064.2.a.f	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(4-\beta _{1}+\beta _{2})q^{9}+\cdots\)
7448.2.a.bj	$7448$	$2$	7448.a	1.a	$1$	$4$	$4$	$59.473$	4.4.25857.1	None	✓				1064.2.a.h	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
7448.2.a.bk	$7448$	$2$	7448.a	1.a	$1$	$4$	$4$	$59.473$	4.4.18097.1	None	✓				1064.2.a.g	$1$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+(1+\beta _{2}-\beta _{3})q^{5}+(2-2\beta _{1}+\cdots)q^{9}+\cdots\)
7448.2.a.bl	$7448$	$2$	7448.a	1.a	$1$	$5$	$5$	$59.473$	5.5.10463409.1	None	✓				1064.2.a.i	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{4})q^{5}+(1+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
7448.2.a.bm	$7448$	$2$	7448.a	1.a	$1$	$6$	$6$	$59.473$	6.6.98211824.1	None	✓	✓	✓		7448.2.a.bm	$1$	$1$	\(0\)	\(-3\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+\beta _{3}q^{5}+(1-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7448.2.a.bn	$7448$	$2$	7448.a	1.a	$1$	$6$	$6$	$59.473$	6.6.98211824.1	None	✓	✓			7448.2.a.bm	$1$	$0$	\(0\)	\(3\)	\(1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-\beta _{3}q^{5}+(1-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7448.2.a.bo	$7448$	$2$	7448.a	1.a	$1$	$7$	$7$	$59.473$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓		7448.2.a.bo	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{5}q^{5}+(1+\beta _{4}+\beta _{5})q^{9}+\cdots\)
7448.2.a.bp	$7448$	$2$	7448.a	1.a	$1$	$7$	$7$	$59.473$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			7448.2.a.bo	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{5}q^{5}+(1+\beta _{4}+\beta _{5})q^{9}+\cdots\)
7448.2.a.bq	$7448$	$2$	7448.a	1.a	$1$	$8$	$8$	$59.473$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				1064.2.q.n	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(1+\beta _{2})q^{9}+(1+\beta _{3}+\cdots)q^{11}+\cdots\)
7448.2.a.br	$7448$	$2$	7448.a	1.a	$1$	$8$	$8$	$59.473$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		1064.2.q.n	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(1+\beta _{2})q^{9}+(1+\beta _{3}+\cdots)q^{11}+\cdots\)
7448.2.a.bs	$7448$	$2$	7448.a	1.a	$1$	$11$	$11$	$59.473$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓		✓		1064.2.q.o	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{4}q^{5}+(2+\beta _{2})q^{9}+(-\beta _{6}+\cdots)q^{11}+\cdots\)
7448.2.a.bt	$7448$	$2$	7448.a	1.a	$1$	$11$	$11$	$59.473$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓				1064.2.q.o	$1$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{4}q^{5}+(2+\beta _{2})q^{9}+(-\beta _{6}+\cdots)q^{11}+\cdots\)
7448.2.a.bu	$7448$	$2$	7448.a	1.a	$1$	$14$	$14$	$59.473$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓	✓		7448.2.a.bu	$1$	$1$	\(0\)	\(-6\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{7}q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
7448.2.a.bv	$7448$	$2$	7448.a	1.a	$1$	$14$	$14$	$59.473$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓	✓		7448.2.a.bv	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{11}q^{5}+(1+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
7448.2.a.bw	$7448$	$2$	7448.a	1.a	$1$	$14$	$14$	$59.473$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓	✓		7448.2.a.bv	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{11}q^{5}+(1+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
7448.2.a.bx	$7448$	$2$	7448.a	1.a	$1$	$14$	$14$	$59.473$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓	✓		7448.2.a.bu	$1$	$0$	\(0\)	\(6\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{7}q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7448))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7448)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(532))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(931))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1064))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1862))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3724))\)\(^{\oplus 2}\)