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 + 4 * q^11 - 12 * q^14 - 2 * q^16 + 4 * q^19 - 8 * q^26 + 16 * q^29 - 20 * q^31 - 4 * q^34 - 4 * q^41 + 16 * q^44 + 24 * q^46 - 26 * q^49 - 28 * q^59 - 16 * q^61 + 18 * q^64 + 32 * q^71 + 28 * q^74 - 24 * q^76 + 8 * q^79 + 4 * q^86 - 12 * q^89 + 44 * q^91 + 8 * q^94

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	Twist minimal	Largest	Maximal	Minimal twist	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					75.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}-2 q^{4}+3 i q^{7}-2 q^{11}+\cdots\)
225.2.b.b	$225$	$2$	225.b	5.b	$2$	$2$	$2$	$1.797$	\(\Q(\sqrt{-1}) \)	None					15.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}+3 i q^{8}+4 q^{11}+2 i q^{13}+\cdots\)
225.2.b.c	$225$	$2$	225.b	5.b	$2$	$2$	$2$	$1.797$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-3}) \)		✓			225.2.a.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5$	$\mathrm{U}(1)[D_{2}]$	\(q+2 q^{4}+\beta q^{7}-\beta q^{13}+4 q^{16}+q^{19}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(225, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)