Space of modular forms of level 810, weight 2, and Character 810.i

• Label: 810.2.i
• Level: $810$
• Weight: $2$
• Character orbit: 810.i
• Rep. character: $\chi_{810}(109,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $48$
• Newform subspaces: $9$
• Sturm bound: $324$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(324\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(810, [\chi])\).

	Total	New	Old
Modular forms	372	48	324
Cusp forms	276	48	228
Eisenstein series	96	0	96

Trace form

\( 48 q + 24 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(810, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
810.2.i.a	$810$	$2$	810.i	45.j	$6$	$4$	$2$	$6.468$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
810.2.i.b	$810$	$2$	810.i	45.j	$6$	$4$	$2$	$6.468$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
810.2.i.c	$810$	$2$	810.i	45.j	$6$	$4$	$2$	$6.468$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(2\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
810.2.i.d	$810$	$2$	810.i	45.j	$6$	$4$	$2$	$6.468$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
810.2.i.e	$810$	$2$	810.i	45.j	$6$	$4$	$2$	$6.468$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(\zeta_{12}+2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
810.2.i.f	$810$	$2$	810.i	45.j	$6$	$4$	$2$	$6.468$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}+2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
810.2.i.g	$810$	$2$	810.i	45.j	$6$	$8$	$4$	$6.468$	8.0.2702336256.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{4}+\beta _{6})q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
810.2.i.h	$810$	$2$	810.i	45.j	$6$	$8$	$4$	$6.468$	8.0.2702336256.1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{4}q^{2}-\beta _{2}q^{4}-\beta _{1}q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
810.2.i.i	$810$	$2$	810.i	45.j	$6$	$8$	$4$	$6.468$	8.0.2702336256.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{4}-\beta _{6})q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(810, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(810, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 2}\)