Space of modular forms of level 405, weight 2, and Character 405.f

• Label: 405.2.f
• Level: $405$
• Weight: $2$
• Character orbit: 405.f
• Rep. character: $\chi_{405}(242,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $40$
• Newform subspaces: $2$
• Sturm bound: $108$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(108\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(405, [\chi])\).

	Total	New	Old
Modular forms	132	56	76
Cusp forms	84	40	44
Eisenstein series	48	16	32

Trace form

\( 40 q + 4 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(405, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
405.2.f.a	$405$	$2$	405.f	15.e	$4$	$16$	$8$	$3.234$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{3}q^{2}+(\beta _{6}-\beta _{14})q^{4}-\beta _{4}q^{5}+\beta _{10}q^{7}+\cdots\)
405.2.f.b	$405$	$2$	405.f	15.e	$4$	$24$	$12$	$3.234$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(405, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(405, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)