Space of modular forms of level 374, weight 2, and Character 374.b

• Label: 374.2.b
• Level: $374$
• Weight: $2$
• Character orbit: 374.b
• Rep. character: $\chi_{374}(67,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $2$
• Sturm bound: $108$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 374 = 2 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	374.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(108\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(374, [\chi])\).

	Total	New	Old
Modular forms	58	14	44
Cusp forms	50	14	36
Eisenstein series	8	0	8

Trace form

\( 14 q + 2 q^{2} + 14 q^{4} + 2 q^{8} - 10 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(374, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
374.2.b.a	$374$	$2$	374.b	17.b	$2$	$6$	$6$	$2.986$	6.0.419904.1	None		$2$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+(\beta _{1}+\beta _{3}+\beta _{5})q^{3}+q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots\)
374.2.b.b	$374$	$2$	374.b	17.b	$2$	$8$	$8$	$2.986$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-\beta _{4}q^{3}+q^{4}+(\beta _{1}-\beta _{5}+\beta _{7})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(374, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(374, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(187, [\chi])\)\(^{\oplus 2}\)