Space of modular forms of level 7504, weight 2, and trivial character

• Label: 7504.2.a
• Level: $7504$
• Weight: $2$
• Character orbit: 7504.a
• Rep. character: $\chi_{7504}(1,\cdot)$
• Character field: $\Q$
• Dimension: $198$
• Newform subspaces: $51$
• Sturm bound: $2176$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 7504 = 2^{4} \cdot 7 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7504.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 51 \)
Sturm bound:			\(2176\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7504))\).

	Total	New	Old
Modular forms	1100	198	902
Cusp forms	1077	198	879
Eisenstein series	23	0	23

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

\(2\)	\(7\)	\(67\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(24\)
\(+\)	\(+\)	\(-\)	$-$	\(25\)
\(+\)	\(-\)	\(+\)	$-$	\(28\)
\(+\)	\(-\)	\(-\)	$+$	\(21\)
\(-\)	\(+\)	\(+\)	$-$	\(27\)
\(-\)	\(+\)	\(-\)	$+$	\(23\)
\(-\)	\(-\)	\(+\)	$+$	\(23\)
\(-\)	\(-\)	\(-\)	$-$	\(27\)
Plus space			\(+\)	\(91\)
Minus space			\(-\)	\(107\)

Trace form

\( 198 q + 4 q^{5} + 198 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7504))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	67
7504.2.a.a	$7504$	$2$	7504.a	1.a	$1$	$1$	$1$	$59.920$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-3\)	\(-3\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-3q^{5}+q^{7}+6q^{9}-2q^{11}+\cdots\)
7504.2.a.b	$7504$	$2$	7504.a	1.a	$1$	$1$	$1$	$59.920$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+3q^{5}+q^{7}+6q^{9}+4q^{11}+\cdots\)
7504.2.a.c	$7504$	$2$	7504.a	1.a	$1$	$1$	$1$	$59.920$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{7}+q^{9}-4q^{13}-2q^{17}+\cdots\)
7504.2.a.d	$7504$	$2$	7504.a	1.a	$1$	$1$	$1$	$59.920$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-1\)	\(-3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+q^{7}-2q^{9}-q^{13}+3q^{15}+\cdots\)
7504.2.a.e	$7504$	$2$	7504.a	1.a	$1$	$1$	$1$	$59.920$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}-2q^{9}-2q^{11}-7q^{13}+\cdots\)
7504.2.a.f	$7504$	$2$	7504.a	1.a	$1$	$1$	$1$	$59.920$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}-2q^{9}+5q^{13}+q^{15}+\cdots\)
7504.2.a.g	$7504$	$2$	7504.a	1.a	$1$	$1$	$1$	$59.920$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}-2q^{9}+2q^{11}+q^{13}+\cdots\)
7504.2.a.h	$7504$	$2$	7504.a	1.a	$1$	$1$	$1$	$59.920$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}-2q^{9}+3q^{13}-q^{15}+\cdots\)
7504.2.a.i	$7504$	$2$	7504.a	1.a	$1$	$1$	$1$	$59.920$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}-2q^{9}+4q^{11}-q^{13}+\cdots\)
7504.2.a.j	$7504$	$2$	7504.a	1.a	$1$	$1$	$1$	$59.920$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}-q^{7}-2q^{9}+5q^{13}+\cdots\)
7504.2.a.k	$7504$	$2$	7504.a	1.a	$1$	$1$	$1$	$59.920$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}-q^{7}-2q^{9}+6q^{11}+\cdots\)
7504.2.a.l	$7504$	$2$	7504.a	1.a	$1$	$1$	$1$	$59.920$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}-3q^{9}+4q^{13}+q^{17}+\cdots\)
7504.2.a.m	$7504$	$2$	7504.a	1.a	$1$	$1$	$1$	$59.920$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-3q^{9}+4q^{11}+4q^{13}+2q^{17}+\cdots\)
7504.2.a.n	$7504$	$2$	7504.a	1.a	$1$	$1$	$1$	$59.920$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}-q^{7}-2q^{9}-q^{13}-3q^{15}+\cdots\)
7504.2.a.o	$7504$	$2$	7504.a	1.a	$1$	$1$	$1$	$59.920$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+q^{7}-2q^{9}+4q^{11}+\cdots\)
7504.2.a.p	$7504$	$2$	7504.a	1.a	$1$	$1$	$1$	$59.920$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}-2q^{9}+4q^{11}-3q^{13}+\cdots\)
7504.2.a.q	$7504$	$2$	7504.a	1.a	$1$	$1$	$1$	$59.920$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}+\cdots\)
7504.2.a.r	$7504$	$2$	7504.a	1.a	$1$	$1$	$1$	$59.920$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}+q^{7}+6q^{9}+4q^{11}+\cdots\)
7504.2.a.s	$7504$	$2$	7504.a	1.a	$1$	$1$	$1$	$59.920$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+q^{5}-q^{7}+6q^{9}-5q^{13}+\cdots\)
7504.2.a.t	$7504$	$2$	7504.a	1.a	$1$	$1$	$1$	$59.920$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+q^{5}+q^{7}+6q^{9}+3q^{13}+\cdots\)
7504.2.a.u	$7504$	$2$	7504.a	1.a	$1$	$1$	$1$	$59.920$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(3\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+3q^{5}+q^{7}+6q^{9}+4q^{11}+\cdots\)
7504.2.a.v	$7504$	$2$	7504.a	1.a	$1$	$2$	$2$	$59.920$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}-q^{7}+2q^{9}+(2+2\beta )q^{11}+\cdots\)
7504.2.a.w	$7504$	$2$	7504.a	1.a	$1$	$2$	$2$	$59.920$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-2+\beta )q^{5}-q^{7}+(1+\beta )q^{9}+\cdots\)
7504.2.a.x	$7504$	$2$	7504.a	1.a	$1$	$2$	$2$	$59.920$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-\beta q^{5}-q^{7}+(1+\beta )q^{9}-4q^{11}+\cdots\)
7504.2.a.y	$7504$	$2$	7504.a	1.a	$1$	$2$	$2$	$59.920$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(3\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(2-\beta )q^{5}+q^{7}+(1+\beta )q^{9}+\cdots\)
7504.2.a.z	$7504$	$2$	7504.a	1.a	$1$	$2$	$2$	$59.920$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-q^{5}-q^{7}+2\beta q^{9}+2\beta q^{11}+\cdots\)
7504.2.a.ba	$7504$	$2$	7504.a	1.a	$1$	$3$	$3$	$59.920$	3.3.321.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-5\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}-q^{7}+\cdots\)
7504.2.a.bb	$7504$	$2$	7504.a	1.a	$1$	$3$	$3$	$59.920$	3.3.316.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+q^{7}+\beta _{2}q^{9}+\cdots\)
7504.2.a.bc	$7504$	$2$	7504.a	1.a	$1$	$3$	$3$	$59.920$	3.3.148.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{5}-q^{7}-3q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)
7504.2.a.bd	$7504$	$2$	7504.a	1.a	$1$	$3$	$3$	$59.920$	3.3.148.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(-9\)	\(-3\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-3q^{5}-q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
7504.2.a.be	$7504$	$2$	7504.a	1.a	$1$	$3$	$3$	$59.920$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(3\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(1+\beta _{2})q^{5}-q^{7}+(2\beta _{1}+\cdots)q^{9}+\cdots\)
7504.2.a.bf	$7504$	$2$	7504.a	1.a	$1$	$4$	$4$	$59.920$	4.4.2777.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(5\)	\(4\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+(1-\beta _{1})q^{5}+q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
7504.2.a.bg	$7504$	$2$	7504.a	1.a	$1$	$4$	$4$	$59.920$	4.4.33844.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(4\)		$+$	$-$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2})q^{5}+q^{7}-3q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)
7504.2.a.bh	$7504$	$2$	7504.a	1.a	$1$	$4$	$4$	$59.920$	4.4.10273.1	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(-\beta _{2}+\beta _{3})q^{5}-q^{7}+\cdots\)
7504.2.a.bi	$7504$	$2$	7504.a	1.a	$1$	$4$	$4$	$59.920$	4.4.2777.1	None	✓	$1$	$1$	\(0\)	\(4\)	\(-6\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2})q^{3}+(-2-\beta _{2}+\beta _{3})q^{5}+\cdots\)
7504.2.a.bj	$7504$	$2$	7504.a	1.a	$1$	$4$	$4$	$59.920$	4.4.15529.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{3}+(\beta _{2}-\beta _{3})q^{5}-q^{7}+(3+\cdots)q^{9}+\cdots\)
7504.2.a.bk	$7504$	$2$	7504.a	1.a	$1$	$5$	$5$	$59.920$	5.5.1891377.1	None	✓	$1$	$1$	\(0\)	\(-4\)	\(-2\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-\beta _{4}q^{5}-q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots\)
7504.2.a.bl	$7504$	$2$	7504.a	1.a	$1$	$5$	$5$	$59.920$	5.5.813209.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(-4\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+q^{7}+\beta _{2}q^{9}+\cdots\)
7504.2.a.bm	$7504$	$2$	7504.a	1.a	$1$	$6$	$6$	$59.920$	6.6.7432373.1	None	✓	$1$	$1$	\(0\)	\(-5\)	\(-3\)	\(6\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
7504.2.a.bn	$7504$	$2$	7504.a	1.a	$1$	$6$	$6$	$59.920$	6.6.769966796.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(6\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{3}-\beta _{1}q^{5}+q^{7}+(3-\beta _{1})q^{9}+\cdots\)
7504.2.a.bo	$7504$	$2$	7504.a	1.a	$1$	$6$	$6$	$59.920$	6.6.98928184.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(0\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(-\beta _{3}-\beta _{5})q^{5}+q^{7}+\cdots\)
7504.2.a.bp	$7504$	$2$	7504.a	1.a	$1$	$7$	$7$	$59.920$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-6\)	\(6\)	\(-7\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{3})q^{3}+(1-\beta _{1}-\beta _{5})q^{5}+\cdots\)
7504.2.a.bq	$7504$	$2$	7504.a	1.a	$1$	$7$	$7$	$59.920$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-6\)	\(7\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+q^{7}+\beta _{2}q^{9}+\cdots\)
7504.2.a.br	$7504$	$2$	7504.a	1.a	$1$	$7$	$7$	$59.920$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-7\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{4}q^{5}-q^{7}+(2+\beta _{2})q^{9}+\cdots\)
7504.2.a.bs	$7504$	$2$	7504.a	1.a	$1$	$9$	$9$	$59.920$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-8\)	\(8\)	\(9\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+(1+\beta _{7})q^{5}+q^{7}+\cdots\)
7504.2.a.bt	$7504$	$2$	7504.a	1.a	$1$	$10$	$10$	$59.920$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(8\)	\(10\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{8})q^{5}+q^{7}+(1+\beta _{5}+\cdots)q^{9}+\cdots\)
7504.2.a.bu	$7504$	$2$	7504.a	1.a	$1$	$10$	$10$	$59.920$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(5\)	\(-10\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1+\beta _{7})q^{5}-q^{7}+(2-\beta _{3}+\cdots)q^{9}+\cdots\)
7504.2.a.bv	$7504$	$2$	7504.a	1.a	$1$	$12$	$12$	$59.920$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-6\)	\(12\)		$+$	$-$	$-$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{6}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots\)
7504.2.a.bw	$7504$	$2$	7504.a	1.a	$1$	$13$	$13$	$59.920$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(13\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{8}q^{5}+q^{7}+(1-\beta _{1}+\beta _{6}+\cdots)q^{9}+\cdots\)
7504.2.a.bx	$7504$	$2$	7504.a	1.a	$1$	$14$	$14$	$59.920$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-14\)		$+$	$+$	$+$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{10}q^{5}-q^{7}+(1+\beta _{2})q^{9}+\cdots\)
7504.2.a.by	$7504$	$2$	7504.a	1.a	$1$	$15$	$15$	$59.920$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(10\)	\(-15\)		$+$	$+$	$-$	$-$	$2^{7}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1-\beta _{6})q^{5}-q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7504))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7504)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(67))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(134))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(268))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(469))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(536))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(938))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1072))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1876))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3752))\)\(^{\oplus 2}\)