Space of modular forms of level 45, weight 2, and Character 45.e

• Label: 45.2.e
• Level: $45$
• Weight: $2$
• Character orbit: 45.e
• Rep. character: $\chi_{45}(16,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $12$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	45.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(12\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(45, [\chi])\).

	Total	New	Old
Modular forms	16	8	8
Cusp forms	8	8	0
Eisenstein series	8	0	8

Trace form

8 * q - 2 * q^2 - 2 * q^3 - 4 * q^4 - 2 * q^5 - 4 * q^6 - 2 * q^7 - 4 * q^9 + 4 * q^11 + 14 * q^12 - 2 * q^13 + 12 * q^14 - 2 * q^15 - 4 * q^16 + 4 * q^17 - 20 * q^18 - 8 * q^19 - 6 * q^20 + 6 * q^22 - 6 * q^23 + 24 * q^24 - 4 * q^25 - 8 * q^26 - 2 * q^27 + 16 * q^28 + 8 * q^29 + 14 * q^30 - 8 * q^31 - 22 * q^32 + 20 * q^33 + 16 * q^35 + 16 * q^36 + 4 * q^37 + 10 * q^38 - 20 * q^39 - 6 * q^40 + 8 * q^41 - 42 * q^42 - 2 * q^43 - 40 * q^44 + 8 * q^45 - 20 * q^47 - 10 * q^48 - 2 * q^50 - 16 * q^51 + 10 * q^52 - 8 * q^53 - 4 * q^54 + 22 * q^57 + 18 * q^58 + 16 * q^59 - 22 * q^60 - 8 * q^61 + 84 * q^62 + 24 * q^63 - 16 * q^64 - 6 * q^65 - 8 * q^66 - 8 * q^67 + 26 * q^68 + 48 * q^69 + 6 * q^70 - 16 * q^71 + 6 * q^72 - 8 * q^73 + 20 * q^74 - 2 * q^75 + 4 * q^76 - 6 * q^77 + 2 * q^78 + 4 * q^79 + 12 * q^80 - 28 * q^81 - 48 * q^82 + 6 * q^83 - 36 * q^84 + 6 * q^85 - 20 * q^86 - 26 * q^87 + 18 * q^88 - 48 * q^89 - 2 * q^90 + 32 * q^91 - 36 * q^92 - 42 * q^93 + 24 * q^94 - 12 * q^95 + 28 * q^96 + 16 * q^97 - 76 * q^98 + 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(45, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
45.2.e.a	$45$	$2$	45.e	9.c	$3$	$2$	$1$	$0.359$	\(\Q(\sqrt{-3}) \)	None		✓			45.2.e.a	$2$	$0$	\(-1\)	\(-3\)	\(1\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
45.2.e.b	$45$	$2$	45.e	9.c	$3$	$6$	$3$	$0.359$	6.0.954288.1	None		✓	✓		45.2.e.b	$2$	$0$	\(-1\)	\(1\)	\(-3\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{2}-\beta _{4}-\beta _{5})q^{2}+\beta _{4}q^{3}+\cdots\)