Space of modular forms of level 1840, weight 3, and Character 1840.k

• Label: 1840.3.k
• Level: $1840$
• Weight: $3$
• Character orbit: 1840.k
• Rep. character: $\chi_{1840}(321,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $5$
• Sturm bound: $864$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1840.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(864\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1840, [\chi])\).

	Total	New	Old
Modular forms	588	96	492
Cusp forms	564	96	468
Eisenstein series	24	0	24

Trace form

\( 96 q + 288 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1840, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1840.3.k.a	$1840$	$3$	1840.k	23.b	$2$	$6$	$6$	$50.136$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}-\beta _{3}q^{5}+(\beta _{2}-\beta _{3}+\beta _{5})q^{7}+\cdots\)
1840.3.k.b	$1840$	$3$	1840.k	23.b	$2$	$10$	$10$	$50.136$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2^{2}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}-\beta _{3}q^{5}+(\beta _{2}+\beta _{3})q^{7}+(-2+\cdots)q^{9}+\cdots\)
1840.3.k.c	$1840$	$3$	1840.k	23.b	$2$	$16$	$16$	$50.136$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}-\beta _{4}q^{5}-\beta _{7}q^{7}+(4+\beta _{2}+\cdots)q^{9}+\cdots\)
1840.3.k.d	$1840$	$3$	1840.k	23.b	$2$	$16$	$16$	$50.136$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+\beta _{2}q^{5}+(\beta _{1}+\beta _{5})q^{7}+(5+\cdots)q^{9}+\cdots\)
1840.3.k.e	$1840$	$3$	1840.k	23.b	$2$	$48$	$48$	$50.136$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(1840, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1840, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(368, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(920, [\chi])\)\(^{\oplus 2}\)