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

• Label: 810.2.c
• Level: $810$
• Weight: $2$
• Character orbit: 810.c
• Rep. character: $\chi_{810}(649,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $7$
• Sturm bound: $324$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(324\)
Trace bound:			\(5\)
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	186	24	162
Cusp forms	138	24	114
Eisenstein series	48	0	48

Trace form

\( 24 q - 24 q^{4} - 6 q^{10} + 24 q^{16} - 18 q^{25} + 24 q^{31} + 12 q^{34} + 6 q^{40} - 12 q^{46} + 36 q^{49} - 24 q^{55} - 24 q^{61} - 24 q^{64} + 12 q^{70} - 6 q^{85} - 12 q^{94}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
810.2.c.a	$810$	$2$	810.c	5.b	$2$	$2$	$2$	$6.468$	\(\Q(\sqrt{-1}) \)	None		✓			810.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+(i-2)q^{5}+i q^{7}+\cdots\)
810.2.c.b	$810$	$2$	810.c	5.b	$2$	$2$	$2$	$6.468$	\(\Q(\sqrt{-1}) \)	None					90.2.i.a	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}+(2 i-1)q^{5}+i q^{7}+\cdots\)
810.2.c.c	$810$	$2$	810.c	5.b	$2$	$2$	$2$	$6.468$	\(\Q(\sqrt{-1}) \)	None					90.2.i.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+(-2 i+1)q^{5}+i q^{7}+\cdots\)
810.2.c.d	$810$	$2$	810.c	5.b	$2$	$2$	$2$	$6.468$	\(\Q(\sqrt{-1}) \)	None		✓			810.2.c.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}+(-i+2)q^{5}+i q^{7}+\cdots\)
810.2.c.e	$810$	$2$	810.c	5.b	$2$	$4$	$4$	$6.468$	\(\Q(i, \sqrt{6})\)	None					90.2.i.b	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-q^{4}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
810.2.c.f	$810$	$2$	810.c	5.b	$2$	$4$	$4$	$6.468$	\(\Q(i, \sqrt{6})\)	None					90.2.i.b	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-q^{4}+(1+\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
810.2.c.g	$810$	$2$	810.c	5.b	$2$	$8$	$8$	$6.468$	8.0.2702336256.1	None		✓	✓		810.2.c.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}-q^{4}+\beta _{7}q^{5}-\beta _{3}q^{7}+\beta _{6}q^{8}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(810, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 2}\)