Space of modular forms of level 1254, weight 2, and Character 1254.g

• Label: 1254.2.g
• Level: $1254$
• Weight: $2$
• Character orbit: 1254.g
• Rep. character: $\chi_{1254}(835,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $2$
• Sturm bound: $480$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1254 = 2 \cdot 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1254.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 209 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(480\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1254, [\chi])\).

	Total	New	Old
Modular forms	248	40	208
Cusp forms	232	40	192
Eisenstein series	16	0	16

Trace form

\( 40 q + 40 q^{4} + 8 q^{5} - 40 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1254, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1254.2.g.a	$1254$	$2$	1254.g	209.d	$2$	$20$	$20$	$10.013$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-20\)	\(0\)	\(4\)	\(0\)	$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{6}q^{3}+q^{4}-\beta _{7}q^{5}-\beta _{6}q^{6}+\cdots\)
1254.2.g.b	$1254$	$2$	1254.g	209.d	$2$	$20$	$20$	$10.013$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(20\)	\(0\)	\(4\)	\(0\)	$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-\beta _{6}q^{3}+q^{4}-\beta _{7}q^{5}-\beta _{6}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1254, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1254, [\chi]) \cong \)