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

• Label: 4410.2.d
• Level: $4410$
• Weight: $2$
• Character orbit: 4410.d
• Rep. character: $\chi_{4410}(4409,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $4$
• Sturm bound: $2016$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4410.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(2016\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(11\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	1072	80	992
Cusp forms	944	80	864
Eisenstein series	128	0	128

Trace form

\( 80 q + 80 q^{4} + O(q^{10}) \)

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.d.a	$4410$	$2$	4410.d	105.g	$2$	$16$	$16$	$35.214$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(-16\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+\beta _{5}q^{5}-q^{8}-\beta _{5}q^{10}+\cdots\)
4410.2.d.b	$4410$	$2$	4410.d	105.g	$2$	$16$	$16$	$35.214$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(16\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+\beta _{10}q^{5}+q^{8}+\beta _{10}q^{10}+\cdots\)
4410.2.d.c	$4410$	$2$	4410.d	105.g	$2$	$24$	$24$	$35.214$		None		$4$	$0$	\(-24\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
4410.2.d.d	$4410$	$2$	4410.d	105.g	$2$	$24$	$24$	$35.214$		None		$4$	$0$	\(24\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(4410, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1470, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2205, [\chi])\)\(^{\oplus 2}\)