Space of modular forms of level 1380, weight 3, and Character 1380.d

• Label: 1380.3.d
• Level: $1380$
• Weight: $3$
• Character orbit: 1380.d
• Rep. character: $\chi_{1380}(781,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $864$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1380.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(864\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1380, [\chi])\).

	Total	New	Old
Modular forms	588	32	556
Cusp forms	564	32	532
Eisenstein series	24	0	24

Trace form

32 * q + 96 * q^9 + 24 * q^13 + 64 * q^23 - 160 * q^25 - 60 * q^29 - 4 * q^31 - 60 * q^35 - 48 * q^39 - 108 * q^41 + 136 * q^47 - 428 * q^49 + 120 * q^55 - 84 * q^59 + 48 * q^69 + 188 * q^71 + 472 * q^73 - 120 * q^77 + 288 * q^81 + 60 * q^85 - 72 * q^87 - 192 * q^93 + 80 * q^95

Decomposition of \(S_{3}^{\mathrm{new}}(1380, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1380.3.d.a	$1380$	$3$	1380.d	23.b	$2$	$32$	$32$	$37.602$		None		✓	✓	✓	1380.3.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(1380, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1380, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(276, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 2}\)