Space of modular forms of level 450, weight 2, and Character 450.s

• Label: 450.2.s
• Level: $450$
• Weight: $2$
• Character orbit: 450.s
• Rep. character: $\chi_{450}(17,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $80$
• Newform subspaces: $4$
• Sturm bound: $180$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.s (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 75 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(180\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(450, [\chi])\).

	Total	New	Old
Modular forms	784	80	704
Cusp forms	656	80	576
Eisenstein series	128	0	128

Trace form

\( 80 q - 8 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(450, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
450.2.s.a	$450$	$2$	450.s	75.l	$20$	$16$	$2$	$3.593$	\(\Q(\zeta_{40})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{20}]$	\(q+\zeta_{40}^{11}q^{2}-\zeta_{40}^{2}q^{4}+(-\zeta_{40}+2\zeta_{40}^{3}+\cdots)q^{5}+\cdots\)
450.2.s.b	$450$	$2$	450.s	75.l	$20$	$16$	$2$	$3.593$	\(\Q(\zeta_{40})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{20}]$	\(q+\zeta_{40}^{11}q^{2}-\zeta_{40}^{2}q^{4}+(-\zeta_{40}^{3}+\cdots)q^{5}+\cdots\)
450.2.s.c	$450$	$2$	450.s	75.l	$20$	$16$	$2$	$3.593$	\(\Q(\zeta_{40})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{20}]$	\(q+\zeta_{40}^{11}q^{2}-\zeta_{40}^{2}q^{4}+(2\zeta_{40}-2\zeta_{40}^{5}+\cdots)q^{5}+\cdots\)
450.2.s.d	$450$	$2$	450.s	75.l	$20$	$32$	$4$	$3.593$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(450, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(450, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)