Space of modular forms of level 45, weight 6, and Character 45.b

• Label: 45.6.b
• Level: $45$
• Weight: $6$
• Character orbit: 45.b
• Rep. character: $\chi_{45}(19,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $4$
• Sturm bound: $36$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	45.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(36\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(45, [\chi])\).

	Total	New	Old
Modular forms	34	14	20
Cusp forms	26	12	14
Eisenstein series	8	2	6

Trace form

12 * q - 204 * q^4 - 30 * q^5 - 360 * q^10 - 840 * q^11 + 2316 * q^14 + 6996 * q^16 - 4032 * q^19 + 180 * q^20 - 2040 * q^25 - 5772 * q^26 + 6756 * q^29 - 11664 * q^31 - 27912 * q^34 - 25320 * q^35 + 69900 * q^40 - 3228 * q^41 + 96084 * q^44 + 22488 * q^46 - 69972 * q^49 - 93000 * q^50 + 88200 * q^55 - 78780 * q^56 + 163992 * q^59 + 83376 * q^61 - 369324 * q^64 - 82680 * q^65 + 72720 * q^70 - 141552 * q^71 + 282276 * q^74 + 298824 * q^76 - 39456 * q^79 - 180060 * q^80 + 12780 * q^85 - 57120 * q^86 + 293508 * q^89 + 147888 * q^91 - 445680 * q^94 - 99960 * q^95

Decomposition of \(S_{6}^{\mathrm{new}}(45, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
45.6.b.a	$45$	$6$	45.b	5.b	$2$	$2$	$2$	$7.217$	\(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{-15}) \)		✓			45.6.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}-93q^{4}+5\beta q^{5}-61\beta q^{8}+\cdots\)
45.6.b.b	$45$	$6$	45.b	5.b	$2$	$2$	$2$	$7.217$	\(\Q(\sqrt{-11}) \)	None					5.6.b.a	$2$	$0$	\(0\)	\(0\)	\(90\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}-12q^{4}+(45-5\beta )q^{5}-9\beta q^{7}+\cdots\)
45.6.b.c	$45$	$6$	45.b	5.b	$2$	$4$	$4$	$7.217$	\(\Q(i, \sqrt{89})\)	None					15.6.b.a	$2$	$0$	\(0\)	\(0\)	\(-120\)	\(0\)	$3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-11+\beta _{3})q^{4}+(-30-5\beta _{1}+\cdots)q^{5}+\cdots\)
45.6.b.d	$45$	$6$	45.b	5.b	$2$	$4$	$4$	$7.217$	\(\Q(\sqrt{-5}, \sqrt{-14})\)	None		✓			45.6.b.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}\cdot 3^{2}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+12q^{4}+(5\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(45, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)