Space of modular forms of level 1890, weight 2, and Character 1890.g

• Label: 1890.2.g
• Level: $1890$
• Weight: $2$
• Character orbit: 1890.g
• Rep. character: $\chi_{1890}(379,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $18$
• Sturm bound: $864$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(864\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(11\), \(13\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1890, [\chi])\).

	Total	New	Old
Modular forms	456	48	408
Cusp forms	408	48	360
Eisenstein series	48	0	48

Trace form

\( 48 q - 48 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1890, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1890.2.g.a	$1890$	$2$	1890.g	5.b	$2$	$2$	$2$	$15.092$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(-2+i)q^{5}-iq^{7}+\cdots\)
1890.2.g.b	$1890$	$2$	1890.g	5.b	$2$	$2$	$2$	$15.092$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(-2-i)q^{5}+iq^{7}+\cdots\)
1890.2.g.c	$1890$	$2$	1890.g	5.b	$2$	$2$	$2$	$15.092$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+(-1-2i)q^{5}-iq^{7}+\cdots\)
1890.2.g.d	$1890$	$2$	1890.g	5.b	$2$	$2$	$2$	$15.092$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+(-1-2i)q^{5}-iq^{7}+\cdots\)
1890.2.g.e	$1890$	$2$	1890.g	5.b	$2$	$2$	$2$	$15.092$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+(-1-2i)q^{5}+iq^{7}+\cdots\)
1890.2.g.f	$1890$	$2$	1890.g	5.b	$2$	$2$	$2$	$15.092$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+(-1-2i)q^{5}+iq^{7}+\cdots\)
1890.2.g.g	$1890$	$2$	1890.g	5.b	$2$	$2$	$2$	$15.092$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(1+2i)q^{5}+iq^{7}-iq^{8}+\cdots\)
1890.2.g.h	$1890$	$2$	1890.g	5.b	$2$	$2$	$2$	$15.092$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+(1-2i)q^{5}-iq^{7}+iq^{8}+\cdots\)
1890.2.g.i	$1890$	$2$	1890.g	5.b	$2$	$2$	$2$	$15.092$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(1+2i)q^{5}-iq^{7}-iq^{8}+\cdots\)
1890.2.g.j	$1890$	$2$	1890.g	5.b	$2$	$2$	$2$	$15.092$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+(1-2i)q^{5}+iq^{7}+iq^{8}+\cdots\)
1890.2.g.k	$1890$	$2$	1890.g	5.b	$2$	$2$	$2$	$15.092$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(2+i)q^{5}+iq^{7}-iq^{8}+\cdots\)
1890.2.g.l	$1890$	$2$	1890.g	5.b	$2$	$2$	$2$	$15.092$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(2-i)q^{5}-iq^{7}-iq^{8}+\cdots\)
1890.2.g.m	$1890$	$2$	1890.g	5.b	$2$	$4$	$4$	$15.092$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-q^{4}+(-1-\beta _{2}-\beta _{3})q^{5}+\cdots\)
1890.2.g.n	$1890$	$2$	1890.g	5.b	$2$	$4$	$4$	$15.092$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}^{3}q^{2}-q^{4}+(2\zeta_{12}-\zeta_{12}^{2}-2\zeta_{12}^{3})q^{5}+\cdots\)
1890.2.g.o	$1890$	$2$	1890.g	5.b	$2$	$4$	$4$	$15.092$	\(\Q(i, \sqrt{10})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-q^{4}-\beta _{1}q^{5}-\beta _{2}q^{7}-\beta _{2}q^{8}+\cdots\)
1890.2.g.p	$1890$	$2$	1890.g	5.b	$2$	$4$	$4$	$15.092$	\(\Q(i, \sqrt{10})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-q^{4}+\beta _{3}q^{5}+\beta _{2}q^{7}-\beta _{2}q^{8}+\cdots\)
1890.2.g.q	$1890$	$2$	1890.g	5.b	$2$	$4$	$4$	$15.092$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}^{3}q^{2}-q^{4}+(1-2\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
1890.2.g.r	$1890$	$2$	1890.g	5.b	$2$	$4$	$4$	$15.092$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-q^{4}+(1+\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1890, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1890, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)