Space of modular forms of level 225, weight 3, and Character 225.c

• Label: 225.3.c
• Level: $225$
• Weight: $3$
• Character orbit: 225.c
• Rep. character: $\chi_{225}(26,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $4$
• Sturm bound: $90$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	225.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(90\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(225, [\chi])\).

	Total	New	Old
Modular forms	72	12	60
Cusp forms	48	12	36
Eisenstein series	24	0	24

Trace form

\( 12 q - 16 q^{4} - 16 q^{7} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(225, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
225.3.c.a	$225$	$3$	225.c	3.b	$2$	$2$	$2$	$6.131$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-18\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+2q^{4}-9q^{7}+6\beta q^{8}+13\beta q^{11}+\cdots\)
225.3.c.b	$225$	$3$	225.c	3.b	$2$	$2$	$2$	$6.131$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(18\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+2q^{4}+9q^{7}+6\beta q^{8}-13\beta q^{11}+\cdots\)
225.3.c.c	$225$	$3$	225.c	3.b	$2$	$4$	$4$	$6.131$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(-3-2\beta _{1})q^{4}+(-4-\beta _{1}+\cdots)q^{7}+\cdots\)
225.3.c.d	$225$	$3$	225.c	3.b	$2$	$4$	$4$	$6.131$	\(\Q(\sqrt{-2}, \sqrt{-7})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-3q^{4}-\beta _{1}q^{7}-\beta _{2}q^{8}-\beta _{3}q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(225, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(225, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)