Space of modular forms of level 4410, weight 2, and Character 4410.b

• Label: 4410.2.b
• Level: $4410$
• Weight: $2$
• Character orbit: 4410.b
• Rep. character: $\chi_{4410}(881,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $6$
• Sturm bound: $2016$
• Trace bound: $22$

Defining parameters

Level:	\( N \)	\(=\)	\( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4410.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(2016\)
Trace bound:			\(22\)
Distinguishing \(T_p\):			\(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4410, [\chi])\).

	Total	New	Old
Modular forms	1072	48	1024
Cusp forms	944	48	896
Eisenstein series	128	0	128

Trace form

\( 48 q - 48 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4410, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4410.2.b.a	$4410$	$2$	4410.b	21.c	$2$	$8$	$8$	$35.214$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{16}q^{2}-q^{4}-q^{5}+\zeta_{16}q^{8}+\zeta_{16}q^{10}+\cdots\)
4410.2.b.b	$4410$	$2$	4410.b	21.c	$2$	$8$	$8$	$35.214$	\(\Q(\zeta_{24})\)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{24}q^{2}-q^{4}-q^{5}+\zeta_{24}q^{8}+\zeta_{24}q^{10}+\cdots\)
4410.2.b.c	$4410$	$2$	4410.b	21.c	$2$	$8$	$8$	$35.214$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{16}q^{2}-q^{4}-q^{5}-\zeta_{16}q^{8}-\zeta_{16}q^{10}+\cdots\)
4410.2.b.d	$4410$	$2$	4410.b	21.c	$2$	$8$	$8$	$35.214$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{16}q^{2}-q^{4}+q^{5}+\zeta_{16}q^{8}-\zeta_{16}q^{10}+\cdots\)
4410.2.b.e	$4410$	$2$	4410.b	21.c	$2$	$8$	$8$	$35.214$	\(\Q(\zeta_{24})\)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{24}q^{2}-q^{4}+q^{5}+\zeta_{24}q^{8}-\zeta_{24}q^{10}+\cdots\)
4410.2.b.f	$4410$	$2$	4410.b	21.c	$2$	$8$	$8$	$35.214$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{16}q^{2}-q^{4}+q^{5}-\zeta_{16}q^{8}+\zeta_{16}q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4410, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4410, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 2}\)