Space of modular forms of level 770, weight 2, and Character 770.c

• Label: 770.2.c
• Level: $770$
• Weight: $2$
• Character orbit: 770.c
• Rep. character: $\chi_{770}(309,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $6$
• Sturm bound: $288$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(288\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(770, [\chi])\).

	Total	New	Old
Modular forms	152	28	124
Cusp forms	136	28	108
Eisenstein series	16	0	16

Trace form

\( 28 q - 28 q^{4} - 4 q^{5} - 12 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(770, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
770.2.c.a	$770$	$2$	770.c	5.b	$2$	$2$	$2$	$6.148$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+(-2+i)q^{5}-iq^{7}+\cdots\)
770.2.c.b	$770$	$2$	770.c	5.b	$2$	$2$	$2$	$6.148$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+(1-2i)q^{5}-iq^{7}+iq^{8}+\cdots\)
770.2.c.c	$770$	$2$	770.c	5.b	$2$	$2$	$2$	$6.148$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(2-i)q^{5}+iq^{7}-iq^{8}+\cdots\)
770.2.c.d	$770$	$2$	770.c	5.b	$2$	$4$	$4$	$6.148$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{2}q^{3}-q^{4}+(-1-2\beta _{1}+\cdots)q^{5}+\cdots\)
770.2.c.e	$770$	$2$	770.c	5.b	$2$	$8$	$8$	$6.148$	8.0.1698758656.6	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+\beta _{4}q^{3}-q^{4}-\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots\)
770.2.c.f	$770$	$2$	770.c	5.b	$2$	$10$	$10$	$6.148$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+\beta _{7}q^{3}-q^{4}+\beta _{5}q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(770, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(770, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)