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

• Label: 810.2.m
• Level: $810$
• Weight: $2$
• Character orbit: 810.m
• Rep. character: $\chi_{810}(53,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $96$
• Newform subspaces: $10$
• Sturm bound: $324$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.m (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(324\)
Trace bound:			\(10\)
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	744	96	648
Cusp forms	552	96	456
Eisenstein series	192	0	192

Trace form

\( 96 q + O(q^{10}) \)

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.m.a	$810$	$2$	810.m	45.l	$12$	$8$	$2$	$6.468$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(-12\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-1+\zeta_{24}^{3}+\cdots)q^{5}+\cdots\)
810.2.m.b	$810$	$2$	810.m	45.l	$12$	$8$	$2$	$6.468$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-20\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{3}-2\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
810.2.m.c	$810$	$2$	810.m	45.l	$12$	$8$	$2$	$6.468$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\zeta_{24}^{3}+\zeta_{24}^{7})q^{2}+(\zeta_{24}^{2}-\zeta_{24}^{6}+\cdots)q^{4}+\cdots\)
810.2.m.d	$810$	$2$	810.m	45.l	$12$	$8$	$2$	$6.468$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(\zeta_{24}-2\zeta_{24}^{7})q^{5}+\cdots\)
810.2.m.e	$810$	$2$	810.m	45.l	$12$	$8$	$2$	$6.468$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\zeta_{24}^{5}q^{2}+(-\zeta_{24}^{2}+\zeta_{24}^{6})q^{4}+\cdots\)
810.2.m.f	$810$	$2$	810.m	45.l	$12$	$8$	$2$	$6.468$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\zeta_{24}^{3}+\zeta_{24}^{7})q^{2}+(\zeta_{24}^{2}-\zeta_{24}^{6}+\cdots)q^{4}+\cdots\)
810.2.m.g	$810$	$2$	810.m	45.l	$12$	$8$	$2$	$6.468$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\zeta_{24}^{5}q^{2}+(-\zeta_{24}^{2}+\zeta_{24}^{6})q^{4}+\cdots\)
810.2.m.h	$810$	$2$	810.m	45.l	$12$	$8$	$2$	$6.468$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(12\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(1-\zeta_{24}^{3}+\cdots)q^{5}+\cdots\)
810.2.m.i	$810$	$2$	810.m	45.l	$12$	$16$	$4$	$6.468$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\beta _{9}q^{2}+(\beta _{5}-\beta _{6})q^{4}+(\beta _{1}+\beta _{9}-\beta _{13}+\cdots)q^{5}+\cdots\)
810.2.m.j	$810$	$2$	810.m	45.l	$12$	$16$	$4$	$6.468$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\beta _{7}q^{2}+(-\beta _{5}+\beta _{6})q^{4}+(\beta _{1}-\beta _{7}+\cdots)q^{5}+\cdots\)

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

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