Space of modular forms of level 225, weight 2, and Character 225.b

• Label: 225.2.b
• Level: $225$
• Weight: $2$
• Character orbit: 225.b
• Rep. character: $\chi_{225}(199,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $3$
• Sturm bound: $60$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(60\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(225, [\chi])\).

	Total	New	Old
Modular forms	42	8	34
Cusp forms	18	6	12
Eisenstein series	24	2	22

Trace form

\( 6 q + 2 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(225, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
225.2.b.a	$225$	$2$	225.b	5.b	$2$	$2$	$2$	$1.797$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-2q^{4}+3iq^{7}-2q^{11}+iq^{13}+\cdots\)
225.2.b.b	$225$	$2$	225.b	5.b	$2$	$2$	$2$	$1.797$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+3iq^{8}+4q^{11}+2iq^{13}+\cdots\)
225.2.b.c	$225$	$2$	225.b	5.b	$2$	$2$	$2$	$1.797$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{4}+iq^{7}-iq^{13}+4q^{16}+q^{19}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(225, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(225, [\chi]) \cong \)