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

• Label: 225.2.p
• Level: $225$
• Weight: $2$
• Character orbit: 225.p
• Rep. character: $\chi_{225}(32,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $64$
• Newform subspaces: $3$
• Sturm bound: $60$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.p (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(60\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	144	80	64
Cusp forms	96	64	32
Eisenstein series	48	16	32

Trace form

\( 64 q + 6 q^{2} + 6 q^{3} - 24 q^{6} + 2 q^{7} + O(q^{10}) \)

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.p.a	$225$	$2$	225.p	45.l	$12$	$16$	$4$	$1.797$	16.0.\(\cdots\).9	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\beta _{6}-\beta _{13})q^{2}+\beta _{1}q^{3}+(-\beta _{9}+\cdots)q^{4}+\cdots\)
225.2.p.b	$225$	$2$	225.p	45.l	$12$	$16$	$4$	$1.797$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(6\)	\(6\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\beta _{5}q^{2}+(1-\beta _{9}+\beta _{11}+\beta _{12}+\beta _{13}+\cdots)q^{3}+\cdots\)
225.2.p.c	$225$	$2$	225.p	45.l	$12$	$32$	$8$	$1.797$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

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

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