Space of modular forms of level 2960, weight 2, and Character 2960.p

• Label: 2960.2.p
• Level: $2960$
• Weight: $2$
• Character orbit: 2960.p
• Rep. character: $\chi_{2960}(961,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $11$
• Sturm bound: $912$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2960 = 2^{4} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2960.p (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(912\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2960, [\chi])\).

	Total	New	Old
Modular forms	468	76	392
Cusp forms	444	76	368
Eisenstein series	24	0	24

Trace form

\( 76 q + 4 q^{3} - 4 q^{7} + 76 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2960, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2960.2.p.a	$2960$	$2$	2960.p	37.b	$2$	$2$	$2$	$23.636$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(-6\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{3}+iq^{5}+q^{7}+6q^{9}-3q^{11}+\cdots\)
2960.2.p.b	$2960$	$2$	2960.p	37.b	$2$	$2$	$2$	$23.636$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(-4\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{3}+iq^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
2960.2.p.c	$2960$	$2$	2960.p	37.b	$2$	$2$	$2$	$23.636$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+iq^{5}-q^{7}-2q^{9}+3q^{11}+\cdots\)
2960.2.p.d	$2960$	$2$	2960.p	37.b	$2$	$2$	$2$	$23.636$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{5}-5q^{7}-3q^{9}-3q^{11}-2iq^{13}+\cdots\)
2960.2.p.e	$2960$	$2$	2960.p	37.b	$2$	$2$	$2$	$23.636$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{5}+2q^{7}-3q^{9}+4q^{11}-2iq^{13}+\cdots\)
2960.2.p.f	$2960$	$2$	2960.p	37.b	$2$	$4$	$4$	$23.636$	\(\Q(i, \sqrt{33})\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{3})q^{3}+\beta _{2}q^{5}-q^{7}+(6-\beta _{3})q^{9}+\cdots\)
2960.2.p.g	$2960$	$2$	2960.p	37.b	$2$	$6$	$6$	$23.636$	6.0.399424.1	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(-10\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{1}+\beta _{3})q^{3}-\beta _{2}q^{5}+(-2-\beta _{3}+\cdots)q^{7}+\cdots\)
2960.2.p.h	$2960$	$2$	2960.p	37.b	$2$	$12$	$12$	$23.636$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(18\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{3}-\beta _{4}q^{5}+(2-\beta _{3}-\beta _{5})q^{7}+\cdots\)
2960.2.p.i	$2960$	$2$	2960.p	37.b	$2$	$12$	$12$	$23.636$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(2\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{3})q^{3}+\beta _{6}q^{5}-\beta _{4}q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots\)
2960.2.p.j	$2960$	$2$	2960.p	37.b	$2$	$12$	$12$	$23.636$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(10\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{3})q^{3}+\beta _{7}q^{5}+(2+\beta _{3}-\beta _{5}+\cdots)q^{7}+\cdots\)
2960.2.p.k	$2960$	$2$	2960.p	37.b	$2$	$20$	$20$	$23.636$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(-6\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{16}q^{3}-\beta _{11}q^{5}+\beta _{8}q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2960, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(592, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(740, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1480, [\chi])\)\(^{\oplus 2}\)