Space of modular forms of level 45, weight 8, and Character 45.b

• Label: 45.8.b
• Level: $45$
• Weight: $8$
• Character orbit: 45.b
• Rep. character: $\chi_{45}(19,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $48$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
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:			\(48\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(45, [\chi])\).

	Total	New	Old
Modular forms	46	18	28
Cusp forms	38	16	22
Eisenstein series	8	2	6

Trace form

16 * q - 924 * q^4 + 294 * q^5 + 464 * q^10 + 2904 * q^11 + 4476 * q^14 + 22676 * q^16 + 19760 * q^19 - 89244 * q^20 + 137116 * q^25 + 574980 * q^26 - 291252 * q^29 - 165520 * q^31 + 412456 * q^34 - 367320 * q^35 - 659252 * q^40 + 558588 * q^41 - 2414700 * q^44 - 396008 * q^46 - 214088 * q^49 + 4247736 * q^50 - 1782504 * q^55 - 1972380 * q^56 - 3969384 * q^59 - 2170744 * q^61 + 7068532 * q^64 + 8019192 * q^65 - 3135600 * q^70 + 2345040 * q^71 - 28776204 * q^74 + 2547816 * q^76 + 9700256 * q^79 + 33457476 * q^80 - 12089908 * q^85 + 35108544 * q^86 - 57067236 * q^89 - 19453968 * q^91 + 45497392 * q^94 + 24745656 * q^95

Decomposition of \(S_{8}^{\mathrm{new}}(45, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
45.8.b.a	$45$	$8$	45.b	5.b	$2$	$2$	$2$	$14.057$	\(\Q(\sqrt{-29}) \)	None					5.8.b.a	$2$	$0$	\(0\)	\(0\)	\(-150\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+12q^{4}+(-75-5^{2}\beta )q^{5}+\cdots\)
45.8.b.b	$45$	$8$	45.b	5.b	$2$	$2$	$2$	$14.057$	\(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{-15}) \)		✓			45.8.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}+123q^{4}+5^{3}\beta q^{5}+251\beta q^{8}+\cdots\)
45.8.b.c	$45$	$8$	45.b	5.b	$2$	$4$	$4$	$14.057$	\(\Q(\sqrt{-65}, \sqrt{85})\)	None		✓			45.8.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-132q^{4}+(-2\beta _{1}+\beta _{3})q^{5}+\cdots\)
45.8.b.d	$45$	$8$	45.b	5.b	$2$	$8$	$8$	$14.057$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None			✓		15.8.b.a	$2$	$0$	\(0\)	\(0\)	\(444\)	\(0\)	$2^{7}\cdot 3^{14}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-83-\beta _{2})q^{4}+(56+4\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(45, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)