Space of modular forms of level 2040, weight 2, and Character 2040.h

• Label: 2040.2.h
• Level: $2040$
• Weight: $2$
• Character orbit: 2040.h
• Rep. character: $\chi_{2040}(1801,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $10$
• Sturm bound: $864$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 2040 = 2^{3} \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2040.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(864\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2040, [\chi])\).

	Total	New	Old
Modular forms	448	36	412
Cusp forms	416	36	380
Eisenstein series	32	0	32

Trace form

\( 36 q - 36 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2040, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2040.2.h.a	$2040$	$2$	2040.h	17.b	$2$	$2$	$2$	$16.289$	\(\Q(\sqrt{-1}) \)	None		✓			2040.2.h.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-iq^{5}+4iq^{7}-q^{9}-4iq^{11}+\cdots\)
2040.2.h.b	$2040$	$2$	2040.h	17.b	$2$	$2$	$2$	$16.289$	\(\Q(\sqrt{-1}) \)	None		✓			2040.2.h.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{5}+4iq^{7}-q^{9}+4iq^{11}+\cdots\)
2040.2.h.c	$2040$	$2$	2040.h	17.b	$2$	$2$	$2$	$16.289$	\(\Q(\sqrt{-1}) \)	None		✓			2040.2.h.c	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+iq^{5}+4iq^{7}-q^{9}-2q^{13}+\cdots\)
2040.2.h.d	$2040$	$2$	2040.h	17.b	$2$	$2$	$2$	$16.289$	\(\Q(\sqrt{-1}) \)	None		✓			2040.2.h.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-iq^{5}+2iq^{7}-q^{9}-2q^{13}+\cdots\)
2040.2.h.e	$2040$	$2$	2040.h	17.b	$2$	$2$	$2$	$16.289$	\(\Q(\sqrt{-1}) \)	None		✓			2040.2.h.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-iq^{5}+iq^{7}-q^{9}-5iq^{11}+\cdots\)
2040.2.h.f	$2040$	$2$	2040.h	17.b	$2$	$2$	$2$	$16.289$	\(\Q(\sqrt{-1}) \)	None		✓			2040.2.h.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{5}+iq^{7}-q^{9}-3iq^{11}+\cdots\)
2040.2.h.g	$2040$	$2$	2040.h	17.b	$2$	$4$	$4$	$16.289$	\(\Q(i, \sqrt{41})\)	None		✓			2040.2.h.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}-q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
2040.2.h.h	$2040$	$2$	2040.h	17.b	$2$	$4$	$4$	$16.289$	\(\Q(i, \sqrt{17})\)	None		✓			2040.2.h.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}-q^{9}+\cdots\)
2040.2.h.i	$2040$	$2$	2040.h	17.b	$2$	$6$	$6$	$16.289$	6.0.399424.1	None		✓			2040.2.h.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+\beta _{2}q^{5}+(2\beta _{2}+\beta _{3})q^{7}-q^{9}+\cdots\)
2040.2.h.j	$2040$	$2$	2040.h	17.b	$2$	$10$	$10$	$16.289$	10.0.\(\cdots\).1	None		✓	✓		2040.2.h.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}-\beta _{4}q^{5}+(\beta _{4}+\beta _{8})q^{7}-q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2040, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2040, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(340, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(408, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(510, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(680, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1020, [\chi])\)\(^{\oplus 2}\)