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

• Label: 690.2.m
• Level: $690$
• Weight: $2$
• Character orbit: 690.m
• Rep. character: $\chi_{690}(31,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $160$
• Newform subspaces: $8$
• 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.m (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(288\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	1520	160	1360
Cusp forms	1360	160	1200
Eisenstein series	160	0	160

Trace form

\( 160 q - 16 q^{4} - 16 q^{9} + O(q^{10}) \)

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.m.a	$690$	$2$	690.m	23.c	$11$	$10$	$1$	$5.510$	\(\Q(\zeta_{22})\)	None		$2$	$0$	\(-1\)	\(-1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+\zeta_{22}^{4}q^{2}+(-1+\zeta_{22}-\zeta_{22}^{2}+\zeta_{22}^{3}+\cdots)q^{3}+\cdots\)
690.2.m.b	$690$	$2$	690.m	23.c	$11$	$10$	$1$	$5.510$	\(\Q(\zeta_{22})\)	None		$2$	$0$	\(1\)	\(-1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q-\zeta_{22}^{4}q^{2}+(-1+\zeta_{22}-\zeta_{22}^{2}+\zeta_{22}^{3}+\cdots)q^{3}+\cdots\)
690.2.m.c	$690$	$2$	690.m	23.c	$11$	$20$	$2$	$5.510$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-2\)	\(2\)	\(-2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+\beta _{16}q^{2}-\beta _{14}q^{3}-\beta _{12}q^{4}+\beta _{11}q^{5}+\cdots\)
690.2.m.d	$690$	$2$	690.m	23.c	$11$	$20$	$2$	$5.510$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-2\)	\(2\)	\(2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+\beta _{7}q^{2}-\beta _{12}q^{3}+\beta _{10}q^{4}-\beta _{6}q^{5}+\cdots\)
690.2.m.e	$690$	$2$	690.m	23.c	$11$	$20$	$2$	$5.510$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(2\)	\(2\)	\(-2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q-\beta _{13}q^{2}-\beta _{16}q^{3}-\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
690.2.m.f	$690$	$2$	690.m	23.c	$11$	$20$	$2$	$5.510$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(2\)	\(2\)	\(2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+\beta _{8}q^{2}+(1+\beta _{5}+\beta _{6}-\beta _{7}-\beta _{8}+\cdots)q^{3}+\cdots\)
690.2.m.g	$690$	$2$	690.m	23.c	$11$	$30$	$3$	$5.510$		None		$2$	$0$	\(-3\)	\(-3\)	\(-3\)	\(-8\)		$\mathrm{SU}(2)[C_{11}]$
690.2.m.h	$690$	$2$	690.m	23.c	$11$	$30$	$3$	$5.510$		None		$2$	$0$	\(3\)	\(-3\)	\(3\)	\(8\)		$\mathrm{SU}(2)[C_{11}]$

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

\( S_{2}^{\mathrm{old}}(690, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 2}\)