Space of modular forms of level 1840, weight 2, and Character 1840.i

• Label: 1840.2.i
• Level: $1840$
• Weight: $2$
• Character orbit: 1840.i
• Rep. character: $\chi_{1840}(1471,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $3$
• Sturm bound: $576$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1840.i (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 92 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(576\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1840, [\chi])\).

	Total	New	Old
Modular forms	300	48	252
Cusp forms	276	48	228
Eisenstein series	24	0	24

Trace form

\( 48 q - 48 q^{9} - 48 q^{25} + 24 q^{29} - 24 q^{41} + 24 q^{49} + 60 q^{69} - 96 q^{77} + 72 q^{81} + 96 q^{93}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1840, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1840.2.i.a	$1840$	$2$	1840.i	92.b	$2$	$16$	$16$	$14.692$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			1840.2.i.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{8}q^{5}+(\beta _{3}-\beta _{10})q^{7}+(-2+\cdots)q^{9}+\cdots\)
1840.2.i.b	$1840$	$2$	1840.i	92.b	$2$	$16$	$16$	$14.692$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			1840.2.i.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{3}+\beta _{2}q^{5}+\beta _{13}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots\)
1840.2.i.c	$1840$	$2$	1840.i	92.b	$2$	$16$	$16$	$14.692$	16.0.\(\cdots\).1	None		✓			1840.2.i.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+\beta _{5}q^{5}+(-\beta _{10}+\beta _{14})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1840, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1840, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(368, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 3}\)