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

• Label: 1840.2.m
• Level: $1840$
• Weight: $2$
• Character orbit: 1840.m
• Rep. character: $\chi_{1840}(1839,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $7$
• Sturm bound: $576$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1840.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 460 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(576\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	300	72	228
Cusp forms	276	72	204
Eisenstein series	24	0	24

Trace form

\( 72 q + 72 q^{9} + 24 q^{29} + 24 q^{41} - 96 q^{49} + 36 q^{69} + 144 q^{81} - 72 q^{85}+O(q^{100}) \)

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.m.a	$1840$	$2$	1840.m	460.g	$2$	$4$	$4$	$14.692$	\(\Q(\sqrt{6}, \sqrt{-14})\)	None		✓			1840.2.m.a	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-\beta _{2}q^{5}-2q^{9}+(2\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots\)
1840.2.m.b	$1840$	$2$	1840.m	460.g	$2$	$4$	$4$	$14.692$	\(\Q(\sqrt{5}, \sqrt{-23})\)	\(\Q(\sqrt{-115}) \)		✓			1840.2.m.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{5}-\beta _{2}q^{7}-3q^{9}+3\beta _{1}q^{17}+\cdots\)
1840.2.m.c	$1840$	$2$	1840.m	460.g	$2$	$4$	$4$	$14.692$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-5}) \)		✓			1840.2.m.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(2\beta _{1}-\beta _{2})q^{3}+\beta _{3}q^{5}+3\beta _{2}q^{7}+\cdots\)
1840.2.m.d	$1840$	$2$	1840.m	460.g	$2$	$4$	$4$	$14.692$	\(\Q(\sqrt{6}, \sqrt{-14})\)	None		✓			1840.2.m.a	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta _{2}q^{5}-2q^{9}+(2\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots\)
1840.2.m.e	$1840$	$2$	1840.m	460.g	$2$	$8$	$8$	$14.692$	8.0.\(\cdots\).1	\(\Q(\sqrt{-115}) \)		✓			1840.2.m.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{5}+\beta _{7}q^{7}-3q^{9}+(-\beta _{1}+\beta _{4}+\cdots)q^{17}+\cdots\)
1840.2.m.f	$1840$	$2$	1840.m	460.g	$2$	$8$	$8$	$14.692$	8.0.40960000.1	None		✓			1840.2.m.f	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+\beta _{6}q^{5}+2\beta _{5}q^{7}+2q^{9}+\cdots\)
1840.2.m.g	$1840$	$2$	1840.m	460.g	$2$	$40$	$40$	$14.692$		None		✓	✓		1840.2.m.g	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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