Space of modular forms of level 225, weight 3, and Character 225.d

• Label: 225.3.d
• Level: $225$
• Weight: $3$
• Character orbit: 225.d
• Rep. character: $\chi_{225}(224,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $90$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	225.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(90\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(225, [\chi])\).

	Total	New	Old
Modular forms	72	12	60
Cusp forms	48	12	36
Eisenstein series	24	0	24

Trace form

\( 12 q + 16 q^{4} + 152 q^{16} - 100 q^{19} - 268 q^{31} - 104 q^{34} + 72 q^{46} + 56 q^{49} - 44 q^{61} + 312 q^{64} - 120 q^{76} + 208 q^{79} + 172 q^{91} + 328 q^{94}+O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(225, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
225.3.d.a	$225$	$3$	225.d	15.d	$2$	$4$	$4$	$6.131$	\(\Q(\zeta_{8})\)	None		✓			225.3.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{3} q^{2}-2 q^{4}+9\beta_1 q^{7}-6\beta_{3} q^{8}+\cdots\)
225.3.d.b	$225$	$3$	225.d	15.d	$2$	$8$	$8$	$6.131$	8.0.40960000.1	None			✓		45.3.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+(3-\beta _{6})q^{4}+(2\beta _{1}-\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(225, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(225, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)