Space of modular forms of level 402, weight 2, and Character 402.d

• Label: 402.2.d
• Level: $402$
• Weight: $2$
• Character orbit: 402.d
• Rep. character: $\chi_{402}(401,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $136$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 402 = 2 \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	402.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 201 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(136\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(402, [\chi])\).

	Total	New	Old
Modular forms	72	24	48
Cusp forms	64	24	40
Eisenstein series	8	0	8

Trace form

\( 24 q + 24 q^{4} - 2 q^{6} + 10 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(402, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
402.2.d.a	$402$	$2$	402.d	201.d	$2$	$12$	$12$	$3.210$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-12\)	\(1\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{8}q^{3}+q^{4}-\beta _{7}q^{5}-\beta _{8}q^{6}+\cdots\)
402.2.d.b	$402$	$2$	402.d	201.d	$2$	$12$	$12$	$3.210$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(12\)	\(-1\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-\beta _{8}q^{3}+q^{4}+\beta _{7}q^{5}-\beta _{8}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(402, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(402, [\chi]) \cong \)