Space of modular forms of level 810, weight 3, and Character 810.j

• Label: 810.3.j
• Level: $810$
• Weight: $3$
• Character orbit: 810.j
• Rep. character: $\chi_{810}(269,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $8$
• Sturm bound: $486$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	810.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(486\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(810, [\chi])\).

	Total	New	Old
Modular forms	696	96	600
Cusp forms	600	96	504
Eisenstein series	96	0	96

Trace form

\( 96 q - 96 q^{4} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(810, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
810.3.j.a	$810$	$3$	810.j	45.h	$6$	$8$	$4$	$22.071$	8.0.\(\cdots\).3	None					270.3.b.a	$4$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}+\beta _{5})q^{2}-2\beta _{4}q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
810.3.j.b	$810$	$3$	810.j	45.h	$6$	$8$	$4$	$22.071$	\(\Q(\zeta_{24})\)	None					270.3.b.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{24}-\zeta_{24}^{7})q^{2}+(-2+2\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)
810.3.j.c	$810$	$3$	810.j	45.h	$6$	$8$	$4$	$22.071$	8.0.\(\cdots\).6	None					30.3.b.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{2}-\beta _{6})q^{2}+(-2+2\beta _{1})q^{4}+\cdots\)
810.3.j.d	$810$	$3$	810.j	45.h	$6$	$8$	$4$	$22.071$	\(\Q(\zeta_{24})\)	None					90.3.b.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{24}-\zeta_{24}^{7})q^{2}+(-2+2\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)
810.3.j.e	$810$	$3$	810.j	45.h	$6$	$8$	$4$	$22.071$	\(\Q(\zeta_{24})\)	None					270.3.b.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{24}-\zeta_{24}^{7})q^{2}+(-2+2\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)
810.3.j.f	$810$	$3$	810.j	45.h	$6$	$8$	$4$	$22.071$	8.0.\(\cdots\).3	None					270.3.b.a	$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{5})q^{2}-2\beta _{4}q^{4}+(\beta _{3}+3\beta _{4}+\cdots)q^{5}+\cdots\)
810.3.j.g	$810$	$3$	810.j	45.h	$6$	$24$	$12$	$22.071$		None		✓			810.3.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-24\)		$\mathrm{SU}(2)[C_{6}]$
810.3.j.h	$810$	$3$	810.j	45.h	$6$	$24$	$12$	$22.071$		None		✓			810.3.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(24\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(810, [\chi])\) into lower level spaces

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