Space of modular forms of level 882, weight 5, and Character 882.c

• Label: 882.5.c
• Level: $882$
• Weight: $5$
• Character orbit: 882.c
• Rep. character: $\chi_{882}(685,\cdot)$
• Character field: $\Q$
• Dimension: $68$
• Newform subspaces: $10$
• Sturm bound: $840$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	882.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(840\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(882, [\chi])\).

	Total	New	Old
Modular forms	704	68	636
Cusp forms	640	68	572
Eisenstein series	64	0	64

Trace form

\( 68 q + 544 q^{4} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(882, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
882.5.c.a	$882$	$5$	882.c	7.b	$2$	$4$	$4$	$91.172$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+8q^{4}+(-11\beta _{2}-\beta _{3})q^{5}+\cdots\)
882.5.c.b	$882$	$5$	882.c	7.b	$2$	$4$	$4$	$91.172$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+8q^{4}+(-9\beta _{2}-2\beta _{3})q^{5}+\cdots\)
882.5.c.c	$882$	$5$	882.c	7.b	$2$	$4$	$4$	$91.172$	4.0.2048.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{2}q^{2}+8q^{4}+(-5\beta _{1}-13\beta _{3})q^{5}+\cdots\)
882.5.c.d	$882$	$5$	882.c	7.b	$2$	$4$	$4$	$91.172$	4.0.2048.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{2}q^{2}+8q^{4}+(19\beta _{1}+13\beta _{3})q^{5}+\cdots\)
882.5.c.e	$882$	$5$	882.c	7.b	$2$	$8$	$8$	$91.172$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+8q^{4}+(-3\beta _{1}-2\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
882.5.c.f	$882$	$5$	882.c	7.b	$2$	$8$	$8$	$91.172$	8.0.339738624.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{1}q^{2}+8q^{4}+(5\beta _{2}-11\beta _{3})q^{5}+\cdots\)
882.5.c.g	$882$	$5$	882.c	7.b	$2$	$8$	$8$	$91.172$	8.0.\(\cdots\).21	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}\cdot 3^{4}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{1}q^{2}+8q^{4}+(-\beta _{3}-4\beta _{4})q^{5}+\cdots\)
882.5.c.h	$882$	$5$	882.c	7.b	$2$	$8$	$8$	$91.172$	8.0.\(\cdots\).21	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}\cdot 3^{4}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{1}q^{2}+8q^{4}+(-\beta _{3}-4\beta _{4})q^{5}+\cdots\)
882.5.c.i	$882$	$5$	882.c	7.b	$2$	$8$	$8$	$91.172$	8.0.339738624.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{4}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{1}q^{2}+8q^{4}+(-5\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
882.5.c.j	$882$	$5$	882.c	7.b	$2$	$12$	$12$	$91.172$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}\cdot 3^{6}\cdot 7^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+8q^{4}-\beta _{3}q^{5}-8\beta _{1}q^{8}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(882, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)