Space of modular forms of level 8820, weight 2, and Character 8820.d

• Label: 8820.2.d
• Level: $8820$
• Weight: $2$
• Character orbit: 8820.d
• Rep. character: $\chi_{8820}(881,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $4$
• Sturm bound: $4032$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 8820 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8820.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(4032\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(8820, [\chi])\).

	Total	New	Old
Modular forms	2112	56	2056
Cusp forms	1920	56	1864
Eisenstein series	192	0	192

Trace form

\( 56 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(8820, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
8820.2.d.a	$8820$	$2$	8820.d	21.c	$2$	$12$	$12$	$70.428$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{5}+(\beta _{1}-\beta _{7})q^{11}-\beta _{8}q^{13}+\beta _{5}q^{17}+\cdots\)
8820.2.d.b	$8820$	$2$	8820.d	21.c	$2$	$12$	$12$	$70.428$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{5}+(\beta _{1}-\beta _{7})q^{11}+\beta _{8}q^{13}-\beta _{5}q^{17}+\cdots\)
8820.2.d.c	$8820$	$2$	8820.d	21.c	$2$	$16$	$16$	$70.428$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-16\)	\(0\)	$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{5}+(-\beta _{10}+\beta _{11}-\beta _{12})q^{11}+\cdots\)
8820.2.d.d	$8820$	$2$	8820.d	21.c	$2$	$16$	$16$	$70.428$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(16\)	\(0\)	$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{5}+(-\beta _{10}+\beta _{11}-\beta _{12})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(8820, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(8820, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1764, [\chi])\)\(^{\oplus 2}\)