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

• Label: 704.2.g
• Level: $704$
• Weight: $2$
• Character orbit: 704.g
• Rep. character: $\chi_{704}(351,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $192$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	704.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 88 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(192\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	108	24	84
Cusp forms	84	24	60
Eisenstein series	24	0	24

Trace form

\( 24 q + 24 q^{9} - 24 q^{25} - 24 q^{33} + 24 q^{49} + 72 q^{81} - 96 q^{97}+O(q^{100}) \)

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	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
704.2.g.a	$704$	$2$	704.g	88.g	$2$	$4$	$4$	$5.621$	\(\Q(i, \sqrt{11})\)	\(\Q(\sqrt{-22}) \)		✓			704.2.g.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-3q^{9}+\beta _{3}q^{11}-\beta _{2}q^{13}+2\beta _{3}q^{19}+\cdots\)
704.2.g.b	$704$	$2$	704.g	88.g	$2$	$4$	$4$	$5.621$	\(\Q(i, \sqrt{11})\)	\(\Q(\sqrt{-11}) \)		✓			704.2.g.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{3}-\beta _{3}q^{5}+8q^{9}+\beta _{2}q^{11}+\cdots\)
704.2.g.c	$704$	$2$	704.g	88.g	$2$	$8$	$8$	$5.621$	\(\Q(\zeta_{24})\)	None		✓			704.2.g.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{4} q^{3}+\beta_{2} q^{5}+\beta_{5} q^{7}+(\beta_{4}+\beta_{3})q^{11}+\cdots\)
704.2.g.d	$704$	$2$	704.g	88.g	$2$	$8$	$8$	$5.621$	\(\Q(i, \sqrt{3}, \sqrt{11})\)	\(\Q(\sqrt{-11}) \)		✓			704.2.g.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta _{3}+\beta _{5})q^{3}+\beta _{1}q^{5}+(1-\beta _{4})q^{9}+\cdots\)

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

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