Space of modular forms of level 774, weight 2, and Character 774.d

• Label: 774.2.d
• Level: $774$
• Weight: $2$
• Character orbit: 774.d
• Rep. character: $\chi_{774}(773,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $264$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 774 = 2 \cdot 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	774.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 129 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(264\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(774, [\chi])\).

	Total	New	Old
Modular forms	140	12	128
Cusp forms	124	12	112
Eisenstein series	16	0	16

Trace form

\( 12 q + 12 q^{4} + 24 q^{13} + 12 q^{16} + 12 q^{25} + 24 q^{31} + 12 q^{43} + 12 q^{49} + 24 q^{52} + 12 q^{64} + 24 q^{67} + 24 q^{79} - 48 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(774, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
774.2.d.a	$774$	$2$	774.d	129.d	$2$	$6$	$6$	$6.180$	6.0.30233088.3	None		✓			774.2.d.a	$2$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+\beta _{4}q^{5}-\beta _{2}q^{7}-q^{8}+\cdots\)
774.2.d.b	$774$	$2$	774.d	129.d	$2$	$6$	$6$	$6.180$	6.0.30233088.3	None		✓			774.2.d.a	$2$	$0$	\(6\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-\beta _{4}q^{5}-\beta _{2}q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(774, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(774, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(129, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(258, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(387, [\chi])\)\(^{\oplus 2}\)