Space of modular forms of level 954, weight 2, and Character 954.c

• Label: 954.2.c
• Level: $954$
• Weight: $2$
• Character orbit: 954.c
• Rep. character: $\chi_{954}(847,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $8$
• Sturm bound: $324$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 954 = 2 \cdot 3^{2} \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	954.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 53 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(324\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(954, [\chi])\).

	Total	New	Old
Modular forms	170	22	148
Cusp forms	154	22	132
Eisenstein series	16	0	16

Trace form

\( 22 q - 22 q^{4} - 4 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(954, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
954.2.c.a	$954$	$2$	954.c	53.b	$2$	$2$	$2$	$7.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+2iq^{5}-2q^{7}-iq^{8}+\cdots\)
954.2.c.b	$954$	$2$	954.c	53.b	$2$	$2$	$2$	$7.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+3iq^{5}-2q^{7}+iq^{8}+\cdots\)
954.2.c.c	$954$	$2$	954.c	53.b	$2$	$2$	$2$	$7.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+q^{7}-iq^{8}-3q^{11}+\cdots\)
954.2.c.d	$954$	$2$	954.c	53.b	$2$	$2$	$2$	$7.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+4iq^{5}+q^{7}+iq^{8}+\cdots\)
954.2.c.e	$954$	$2$	954.c	53.b	$2$	$2$	$2$	$7.618$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+iq^{5}+4q^{7}+iq^{8}+\cdots\)
954.2.c.f	$954$	$2$	954.c	53.b	$2$	$4$	$4$	$7.618$	\(\Q(i, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-q^{4}+\beta _{1}q^{5}-2q^{7}+\beta _{1}q^{8}+\cdots\)
954.2.c.g	$954$	$2$	954.c	53.b	$2$	$4$	$4$	$7.618$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-q^{4}+(\beta _{1}-\beta _{2})q^{5}-2\beta _{3}q^{7}+\cdots\)
954.2.c.h	$954$	$2$	954.c	53.b	$2$	$4$	$4$	$7.618$	\(\Q(i, \sqrt{37})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-q^{4}-2\beta _{1}q^{5}+q^{7}+\beta _{1}q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(954, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(954, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(53, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(106, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(159, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(318, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(477, [\chi])\)\(^{\oplus 2}\)