Space of modular forms of level 704, weight 2, and Character 704.c

• Label: 704.2.c
• Level: $704$
• Weight: $2$
• Character orbit: 704.c
• Rep. character: $\chi_{704}(353,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $3$
• Sturm bound: $192$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	704.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(192\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(704, [\chi])\).

	Total	New	Old
Modular forms	108	20	88
Cusp forms	84	20	64
Eisenstein series	24	0	24

Trace form

\( 20 q - 20 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(704, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
704.2.c.a	$704$	$2$	704.c	8.b	$2$	$4$	$4$	$5.621$	\(\Q(\zeta_{12})\)	None		✓	704.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}+2q^{9}+\zeta_{12}q^{11}+\cdots\)
704.2.c.b	$704$	$2$	704.c	8.b	$2$	$4$	$4$	$5.621$	\(\Q(\zeta_{12})\)	None		✓	704.2.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}-2\zeta_{12}^{3}q^{7}+\cdots\)
704.2.c.c	$704$	$2$	704.c	8.b	$2$	$12$	$12$	$5.621$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	704.2.c.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}-\beta _{7}q^{5}-\beta _{9}q^{7}+(-3+\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(704, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(704, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(352, [\chi])\)\(^{\oplus 2}\)