Space of modular forms of level 462, weight 2, and Character 462.c

• Label: 462.2.c
• Level: $462$
• Weight: $2$
• Character orbit: 462.c
• Rep. character: $\chi_{462}(197,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(462, [\chi])\).

	Total	New	Old
Modular forms	104	24	80
Cusp forms	88	24	64
Eisenstein series	16	0	16

Trace form

\( 24 q + 8 q^{3} + 24 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(462, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
462.2.c.a	$462$	$2$	462.c	33.d	$2$	$12$	$12$	$3.689$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(-12\)	\(4\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{6}q^{3}+q^{4}-\beta _{11}q^{5}-\beta _{6}q^{6}+\cdots\)
462.2.c.b	$462$	$2$	462.c	33.d	$2$	$12$	$12$	$3.689$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(12\)	\(4\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta _{6}q^{3}+q^{4}-\beta _{11}q^{5}+\beta _{6}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(462, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(462, [\chi]) \cong \)