Space of modular forms of level 405, weight 4, and Character 405.b

• Label: 405.4.b
• Level: $405$
• Weight: $4$
• Character orbit: 405.b
• Rep. character: $\chi_{405}(244,\cdot)$
• Character field: $\Q$
• Dimension: $68$
• Newform subspaces: $6$
• Sturm bound: $216$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	405.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(216\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(405, [\chi])\).

	Total	New	Old
Modular forms	174	76	98
Cusp forms	150	68	82
Eisenstein series	24	8	16

Trace form

\( 68 q - 252 q^{4} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(405, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
405.4.b.a	$405$	$4$	405.b	5.b	$2$	$4$	$4$	$23.896$	\(\Q(\sqrt{3}, \sqrt{-17})\)	None		$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2\beta _{1}-\beta _{2})q^{2}-9q^{4}+5\beta _{1}q^{5}+\cdots\)
405.4.b.b	$405$	$4$	405.b	5.b	$2$	$8$	$8$	$23.896$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-15\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-3+\beta _{2})q^{4}+(-2+\beta _{4}+\cdots)q^{5}+\cdots\)
405.4.b.c	$405$	$4$	405.b	5.b	$2$	$8$	$8$	$23.896$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(15\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-3+\beta _{2})q^{4}+(2-\beta _{3})q^{5}+\cdots\)
405.4.b.d	$405$	$4$	405.b	5.b	$2$	$16$	$16$	$23.896$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(-4-\beta _{1})q^{4}+(-\beta _{4}+\beta _{11}+\cdots)q^{5}+\cdots\)
405.4.b.e	$405$	$4$	405.b	5.b	$2$	$16$	$16$	$23.896$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$2^{2}\cdot 3^{12}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-3+\beta _{2})q^{4}+\beta _{9}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
405.4.b.f	$405$	$4$	405.b	5.b	$2$	$16$	$16$	$23.896$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$2^{2}\cdot 3^{12}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-3+\beta _{2})q^{4}+\beta _{8}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(405, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(405, [\chi]) \cong \)