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

• Label: 2340.2.h
• Level: $2340$
• Weight: $2$
• Character orbit: 2340.h
• Rep. character: $\chi_{2340}(469,\cdot)$
• Character field: $\Q$
• Dimension: $30$
• Newform subspaces: $6$
• Sturm bound: $1008$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2340.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1008\)
Trace bound:			\(5\)
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	30	498
Cusp forms	480	30	450
Eisenstein series	48	0	48

Trace form

\( 30 q + 4 q^{5} - 8 q^{11} - 4 q^{19} + 10 q^{25} - 4 q^{29} - 16 q^{31} + 12 q^{35} - 8 q^{41} - 6 q^{49} + 4 q^{55} - 36 q^{59} - 4 q^{61} - 2 q^{65} + 4 q^{71} - 16 q^{79} - 12 q^{85} + 60 q^{89} + 4 q^{95}+O(q^{100}) \)

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.h.a	$2340$	$2$	2340.h	5.b	$2$	$2$	$2$	$18.685$	\(\Q(\sqrt{-1}) \)	None					780.2.h.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2 i-1)q^{5}+3 i q^{7}-3 q^{11}+\cdots\)
2340.2.h.b	$2340$	$2$	2340.h	5.b	$2$	$2$	$2$	$18.685$	\(\Q(\sqrt{-1}) \)	None					780.2.h.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2 i+1)q^{5}+i q^{7}+3 q^{11}+i q^{13}+\cdots\)
2340.2.h.c	$2340$	$2$	2340.h	5.b	$2$	$4$	$4$	$18.685$	\(\Q(\zeta_{8})\)	None					780.2.h.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}-2\zeta_{8}^{3})q^{5}+(2\zeta_{8}+2\zeta_{8}^{2}+2\zeta_{8}^{3})q^{7}+\cdots\)
2340.2.h.d	$2340$	$2$	2340.h	5.b	$2$	$4$	$4$	$18.685$	\(\Q(i, \sqrt{6})\)	None					780.2.h.c	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{2}-\beta _{3})q^{5}-2\beta _{2}q^{7}+(-2+\cdots)q^{11}+\cdots\)
2340.2.h.e	$2340$	$2$	2340.h	5.b	$2$	$6$	$6$	$18.685$	6.0.350464.1	None					260.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{4})q^{5}+(\beta _{3}+\beta _{4}-\beta _{5})q^{7}+\cdots\)
2340.2.h.f	$2340$	$2$	2340.h	5.b	$2$	$12$	$12$	$18.685$	12.0.\(\cdots\).1	None		✓	✓		2340.2.h.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{5}-\beta _{4}q^{7}+(\beta _{3}+\beta _{6}+\beta _{8})q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2340, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1170, [\chi])\)\(^{\oplus 2}\)