Space of modular forms of level 690, weight 2, and Character 690.e

• Label: 690.2.e
• Level: $690$
• Weight: $2$
• Character orbit: 690.e
• Rep. character: $\chi_{690}(551,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 69 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(690, [\chi])\).

	Total	New	Old
Modular forms	152	32	120
Cusp forms	136	32	104
Eisenstein series	16	0	16

Trace form

\( 32 q - 32 q^{4} + 4 q^{6} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(690, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
690.2.e.a	$690$	$2$	690.e	69.c	$2$	$16$	$16$	$5.510$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-16\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{2}+\beta _{2}q^{3}-q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
690.2.e.b	$690$	$2$	690.e	69.c	$2$	$16$	$16$	$5.510$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(16\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{2}+\beta _{2}q^{3}-q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(690, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(690, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 2}\)