Space of modular forms of level 704, weight 6, and Character 704.c

• Label: 704.6.c
• Level: $704$
• Weight: $6$
• Character orbit: 704.c
• Rep. character: $\chi_{704}(353,\cdot)$
• Character field: $\Q$
• Dimension: $100$
• Newform subspaces: $4$
• Sturm bound: $576$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	704.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(576\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(704, [\chi])\).

	Total	New	Old
Modular forms	492	100	392
Cusp forms	468	100	368
Eisenstein series	24	0	24

Trace form

\( 100 q - 8100 q^{9} + 2424 q^{17} - 43804 q^{25} + 14856 q^{41} + 298628 q^{49} + 51552 q^{57} + 23040 q^{65} + 180056 q^{73} + 1194180 q^{81} - 172776 q^{89} + 187672 q^{97}+O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(704, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
704.6.c.a	$704$	$6$	704.c	8.b	$2$	$16$	$16$	$112.910$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			704.6.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{22}\cdot 3^{2}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(4\beta _{8}-\beta _{11})q^{3}+\beta _{3}q^{5}+\beta _{12}q^{7}+\cdots\)
704.6.c.b	$704$	$6$	704.c	8.b	$2$	$20$	$20$	$112.910$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			704.6.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{36}\cdot 5^{4}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(3\beta _{10}-\beta _{14})q^{3}+\beta _{3}q^{5}-\beta _{11}q^{7}+\cdots\)
704.6.c.c	$704$	$6$	704.c	8.b	$2$	$28$	$28$	$112.910$		None		✓			704.6.c.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
704.6.c.d	$704$	$6$	704.c	8.b	$2$	$36$	$36$	$112.910$		None		✓	✓		704.6.c.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{6}^{\mathrm{old}}(704, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(704, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(352, [\chi])\)\(^{\oplus 2}\)