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

• Label: 225.2.e
• Level: $225$
• Weight: $2$
• Character orbit: 225.e
• Rep. character: $\chi_{225}(76,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $32$
• 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.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
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	72	44	28
Cusp forms	48	32	16
Eisenstein series	24	12	12

Trace form

32 * q + 2 * q^2 + 2 * q^3 - 12 * q^4 + 2 * q^7 + 6 * q^9 - 6 * q^11 - 14 * q^12 + 2 * q^13 + 6 * q^14 - 8 * q^16 - 4 * q^17 + 20 * q^18 + 8 * q^19 - 18 * q^21 - 6 * q^22 + 6 * q^23 - 54 * q^24 - 24 * q^26 + 2 * q^27 - 16 * q^28 - 6 * q^29 + 4 * q^31 + 22 * q^32 - 20 * q^33 - 14 * q^34 - 12 * q^36 - 4 * q^37 - 10 * q^38 + 42 * q^39 - 6 * q^41 + 42 * q^42 + 2 * q^43 + 72 * q^44 - 16 * q^46 + 20 * q^47 + 10 * q^48 + 10 * q^49 - 30 * q^51 - 10 * q^52 + 8 * q^53 + 48 * q^54 + 48 * q^56 - 22 * q^57 - 18 * q^58 - 42 * q^59 + 10 * q^61 - 84 * q^62 - 24 * q^63 + 28 * q^64 + 36 * q^66 + 8 * q^67 - 26 * q^68 - 18 * q^69 + 24 * q^71 - 6 * q^72 + 8 * q^73 - 48 * q^74 - 30 * q^76 + 6 * q^77 - 2 * q^78 + 2 * q^79 + 42 * q^81 + 48 * q^82 - 6 * q^83 + 54 * q^84 + 12 * q^86 + 26 * q^87 - 18 * q^88 - 60 * q^89 - 60 * q^91 + 36 * q^92 + 42 * q^93 - 2 * q^94 + 36 * q^96 - 16 * q^97 + 76 * q^98 + 18 * q^99

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.e.a	$225$	$2$	225.e	9.c	$3$	$2$	$1$	$1.797$	\(\Q(\sqrt{-3}) \)	None					45.2.e.a	$2$	$0$	\(1\)	\(3\)	\(0\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
225.2.e.b	$225$	$2$	225.e	9.c	$3$	$6$	$3$	$1.797$	6.0.954288.1	None					45.2.e.b	$2$	$0$	\(1\)	\(-1\)	\(0\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{2}+\beta _{4}+\beta _{5})q^{2}-\beta _{4}q^{3}+\cdots\)
225.2.e.c	$225$	$2$	225.e	9.c	$3$	$8$	$4$	$1.797$	8.0.1223810289.2	None		✓			225.2.e.c	$2$	$0$	\(-2\)	\(1\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-\beta _{4}+\beta _{7})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
225.2.e.d	$225$	$2$	225.e	9.c	$3$	$8$	$4$	$1.797$	\(\Q(\zeta_{24})\)	None					45.2.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta_{7} q^{2}+(-\beta_{7}+\beta_{6})q^{3}-\beta_{2} q^{4}+\cdots\)
225.2.e.e	$225$	$2$	225.e	9.c	$3$	$8$	$4$	$1.797$	8.0.1223810289.2	None		✓			225.2.e.c	$2$	$0$	\(2\)	\(-1\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(\beta _{4}-\beta _{7})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)

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

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