Space of modular forms of level 45, weight 10, and Character 45.b

• Label: 45.10.b
• Level: $45$
• Weight: $10$
• Character orbit: 45.b
• Rep. character: $\chi_{45}(19,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $4$
• Sturm bound: $60$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
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:			\(60\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(45, [\chi])\).

	Total	New	Old
Modular forms	58	24	34
Cusp forms	50	22	28
Eisenstein series	8	2	6

Trace form

\( 22 q - 5292 q^{4} - 450 q^{5} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(45, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
45.10.b.a	$45$	$10$	45.b	5.b	$2$	$2$	$2$	$23.177$	\(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{-15}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+19\beta q^{2}-1293q^{4}-5^{4}\beta q^{5}-14839\beta q^{8}+\cdots\)
45.10.b.b	$45$	$10$	45.b	5.b	$2$	$4$	$4$	$23.177$	4.0.49740556.1	None		$2$	$0$	\(0\)	\(0\)	\(-1140\)	\(0\)	$2^{5}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-342-\beta _{3})q^{4}+(-285+\cdots)q^{5}+\cdots\)
45.10.b.c	$45$	$10$	45.b	5.b	$2$	$8$	$8$	$23.177$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(690\)	\(0\)	$2^{5}\cdot 3^{12}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+(-149-\beta _{1})q^{4}+(86+2\beta _{1}+\cdots)q^{5}+\cdots\)
45.10.b.d	$45$	$10$	45.b	5.b	$2$	$8$	$8$	$23.177$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}\cdot 3^{8}\cdot 5^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-18+\beta _{2})q^{4}+(24\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(45, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)