Space of modular forms of level 1740, weight 2, and Character 1740.l

• Label: 1740.2.l
• Level: $1740$
• Weight: $2$
• Character orbit: 1740.l
• Rep. character: $\chi_{1740}(1681,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $4$
• Sturm bound: $720$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1740 = 2^{2} \cdot 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1740.l (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(720\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1740, [\chi])\).

	Total	New	Old
Modular forms	372	20	352
Cusp forms	348	20	328
Eisenstein series	24	0	24

Trace form

20 * q - 20 * q^9 + 8 * q^13 + 8 * q^23 + 20 * q^25 - 16 * q^29 + 8 * q^35 + 28 * q^49 + 24 * q^51 + 32 * q^53 + 8 * q^57 - 8 * q^59 + 24 * q^67 + 48 * q^71 + 20 * q^81 - 16 * q^83 + 8 * q^87 - 88 * q^91 + 24 * q^93

Decomposition of \(S_{2}^{\mathrm{new}}(1740, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1740.2.l.a	$1740$	$2$	1740.l	29.b	$2$	$2$	$2$	$13.894$	\(\Q(\sqrt{-1}) \)	None		✓			1740.2.l.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+q^{5}+q^{7}-q^{9}-3 i q^{11}+\cdots\)
1740.2.l.b	$1740$	$2$	1740.l	29.b	$2$	$2$	$2$	$13.894$	\(\Q(\sqrt{-1}) \)	None		✓			1740.2.l.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+q^{5}+4 q^{7}-q^{9}-3 i q^{11}+\cdots\)
1740.2.l.c	$1740$	$2$	1740.l	29.b	$2$	$6$	$6$	$13.894$	6.0.399424.1	None		✓			1740.2.l.c	$2$	$0$	\(0\)	\(0\)	\(6\)	\(-6\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+q^{5}+(-1-\beta _{1})q^{7}-q^{9}+\cdots\)
1740.2.l.d	$1740$	$2$	1740.l	29.b	$2$	$10$	$10$	$13.894$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		✓	✓		1740.2.l.d	$2$	$0$	\(0\)	\(0\)	\(-10\)	\(-4\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}-q^{5}+\beta _{1}q^{7}-q^{9}+(-\beta _{4}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1740, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1740, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(174, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(290, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(348, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(435, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(580, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(870, [\chi])\)\(^{\oplus 2}\)