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

• Label: 225.2.m
• Level: $225$
• Weight: $2$
• Character orbit: 225.m
• Rep. character: $\chi_{225}(19,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $48$
• Newform subspaces: $3$
• Sturm bound: $60$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.m (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(60\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	136	56	80
Cusp forms	104	48	56
Eisenstein series	32	8	24

Trace form

\( 48 q + 5 q^{2} + 9 q^{4} + 20 q^{8} + O(q^{10}) \)

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.m.a	$225$	$2$	225.m	25.e	$10$	$8$	$2$	$1.797$	8.0.58140625.2	None		$2$	$0$	\(5\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
225.2.m.b	$225$	$2$	225.m	25.e	$10$	$16$	$4$	$1.797$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(\beta _{1}-\beta _{3}+\beta _{4}-\beta _{10}+\beta _{15})q^{2}+\cdots\)
225.2.m.c	$225$	$2$	225.m	25.e	$10$	$24$	$6$	$1.797$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

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

\( S_{2}^{\mathrm{old}}(225, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)