Space of modular forms of level 2340, weight 2, and Character 2340.c

• Label: 2340.2.c
• Level: $2340$
• Weight: $2$
• Character orbit: 2340.c
• Rep. character: $\chi_{2340}(181,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $5$
• Sturm bound: $1008$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2340.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(1008\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2340, [\chi])\).

	Total	New	Old
Modular forms	528	22	506
Cusp forms	480	22	458
Eisenstein series	48	0	48

Trace form

\( 22 q + 16 q^{17} - 12 q^{23} - 22 q^{25} + 4 q^{29} - 8 q^{35} - 36 q^{43} + 2 q^{49} - 4 q^{53} - 12 q^{55} - 20 q^{61} - 2 q^{65} + 28 q^{77} + 16 q^{79} + 4 q^{91} + 16 q^{95}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2340, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2340.2.c.a	$2340$	$2$	2340.c	13.b	$2$	$2$	$2$	$18.685$	\(\Q(\sqrt{-1}) \)	None					780.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{5}+5 i q^{7}+3 i q^{11}+(3 i-2)q^{13}+\cdots\)
2340.2.c.b	$2340$	$2$	2340.c	13.b	$2$	$2$	$2$	$18.685$	\(\Q(\sqrt{-1}) \)	None					780.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{5}-2 i q^{11}+(-2 i+3)q^{13}+\cdots\)
2340.2.c.c	$2340$	$2$	2340.c	13.b	$2$	$4$	$4$	$18.685$	\(\Q(i, \sqrt{17})\)	None					780.2.c.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}+\beta _{1}q^{7}+(-\beta _{1}+2\beta _{2})q^{11}+\cdots\)
2340.2.c.d	$2340$	$2$	2340.c	13.b	$2$	$6$	$6$	$18.685$	6.0.9144576.1	None					260.2.f.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}+(-\beta _{1}-\beta _{5})q^{7}+(-2\beta _{2}+\cdots)q^{11}+\cdots\)
2340.2.c.e	$2340$	$2$	2340.c	13.b	$2$	$8$	$8$	$18.685$	8.0.2732361984.1	None		✓	✓		2340.2.c.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{5}-\beta _{6}q^{7}+(-\beta _{1}-\beta _{5})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2340, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2340, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1170, [\chi])\)\(^{\oplus 2}\)