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

• Label: 225.2.h
• Level: $225$
• Weight: $2$
• Character orbit: 225.h
• Rep. character: $\chi_{225}(46,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $44$
• Newform subspaces: $5$
• Sturm bound: $60$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 5 \)
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	136	52	84
Cusp forms	104	44	60
Eisenstein series	32	8	24

Trace form

\( 44 q + 4 q^{2} - 12 q^{4} + 11 q^{5} - 10 q^{7} - 7 q^{8} + O(q^{10}) \)

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.h.a	$225$	$2$	225.h	25.d	$5$	$4$	$1$	$1.797$	\(\Q(\zeta_{10})\)	None		$2$	$0$	\(1\)	\(0\)	\(-5\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{4}+\cdots\)
225.2.h.b	$225$	$2$	225.h	25.d	$5$	$4$	$1$	$1.797$	\(\Q(\zeta_{10})\)	None		$2$	$0$	\(2\)	\(0\)	\(5\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+(-1+\zeta_{10}+\zeta_{10}^{3})q^{4}+\cdots\)
225.2.h.c	$225$	$2$	225.h	25.d	$5$	$8$	$2$	$1.797$	8.0.26265625.1	None		$2$	$0$	\(1\)	\(0\)	\(5\)	\(4\)	$5$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{3}+\beta _{7})q^{2}+(-1+2\beta _{1}+2\beta _{3}+\cdots)q^{4}+\cdots\)
225.2.h.d	$225$	$2$	225.h	25.d	$5$	$12$	$3$	$1.797$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{5}-2\beta _{8}+\beta _{9}+\cdots)q^{4}+\cdots\)
225.2.h.e	$225$	$2$	225.h	25.d	$5$	$16$	$4$	$1.797$	16.0.\(\cdots\).3	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{3}-\beta _{10}+\beta _{12}-\beta _{14})q^{2}+(-\beta _{8}+\cdots)q^{4}+\cdots\)

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

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