Space of modular forms of level 45, weight 3, and Character 45.g

• Label: 45.3.g
• Level: $45$
• Weight: $3$
• Character orbit: 45.g
• Rep. character: $\chi_{45}(28,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $18$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	45.g (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(18\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(45, [\chi])\).

	Total	New	Old
Modular forms	32	12	20
Cusp forms	16	8	8
Eisenstein series	16	4	12

Trace form

8 * q + 4 * q^2 + 4 * q^5 - 16 * q^7 - 12 * q^8 - 16 * q^10 - 16 * q^11 + 8 * q^13 + 56 * q^16 + 40 * q^17 + 36 * q^20 - 80 * q^22 - 56 * q^23 - 64 * q^25 - 88 * q^26 + 64 * q^28 + 16 * q^31 + 76 * q^32 + 40 * q^35 + 104 * q^37 + 96 * q^38 + 168 * q^40 + 56 * q^41 + 32 * q^43 - 176 * q^46 - 128 * q^47 - 164 * q^50 - 40 * q^52 - 56 * q^53 - 224 * q^55 - 312 * q^58 - 32 * q^61 - 88 * q^62 + 112 * q^65 + 80 * q^67 + 104 * q^68 + 240 * q^70 + 272 * q^71 + 296 * q^73 + 240 * q^76 - 88 * q^77 - 164 * q^80 + 328 * q^82 + 16 * q^83 + 272 * q^85 + 224 * q^86 - 288 * q^88 - 416 * q^91 - 104 * q^92 - 144 * q^95 - 40 * q^97 + 188 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(45, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
45.3.g.a	$45$	$3$	45.g	5.c	$4$	$4$	$2$	$1.226$	\(\Q(i, \sqrt{10})\)	None		✓			45.3.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-20\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(2\beta _{1}+\beta _{3})q^{5}+(-5+\cdots)q^{7}+\cdots\)
45.3.g.b	$45$	$3$	45.g	5.c	$4$	$4$	$2$	$1.226$	\(\Q(i, \sqrt{6})\)	None					15.3.f.a	$2$	$0$	\(4\)	\(0\)	\(4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{1}+\beta _{2})q^{2}+(2\beta _{1}+\beta _{2}+2\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

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