Space of modular forms of level 1870, weight 2, and Character 1870.b

• Label: 1870.2.b
• Level: $1870$
• Weight: $2$
• Character orbit: 1870.b
• Rep. character: $\chi_{1870}(749,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $6$
• Sturm bound: $648$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1870 = 2 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1870.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(648\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1870, [\chi])\).

	Total	New	Old
Modular forms	332	80	252
Cusp forms	316	80	236
Eisenstein series	16	0	16

Trace form

\( 80 q - 80 q^{4} - 4 q^{5} + 8 q^{6} - 80 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1870, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1870.2.b.a	$1870$	$2$	1870.b	5.b	$2$	$2$	$2$	$14.932$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+2iq^{3}-q^{4}+(1-2i)q^{5}+\cdots\)
1870.2.b.b	$1870$	$2$	1870.b	5.b	$2$	$2$	$2$	$14.932$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+2iq^{3}-q^{4}+(1-2i)q^{5}+\cdots\)
1870.2.b.c	$1870$	$2$	1870.b	5.b	$2$	$10$	$10$	$14.932$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{9}q^{3}-q^{4}+(\beta _{1}+\beta _{7})q^{5}+\cdots\)
1870.2.b.d	$1870$	$2$	1870.b	5.b	$2$	$14$	$14$	$14.932$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{8}q^{2}-\beta _{1}q^{3}-q^{4}+(\beta _{4}+\beta _{7}+\beta _{11}+\cdots)q^{5}+\cdots\)
1870.2.b.e	$1870$	$2$	1870.b	5.b	$2$	$26$	$26$	$14.932$		None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1870.2.b.f	$1870$	$2$	1870.b	5.b	$2$	$26$	$26$	$14.932$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1870, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1870, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(935, [\chi])\)\(^{\oplus 2}\)