Space of modular forms of level 405, weight 5, and Character 405.d

• Label: 405.5.d
• Level: $405$
• Weight: $5$
• Character orbit: 405.d
• Rep. character: $\chi_{405}(404,\cdot)$
• Character field: $\Q$
• Dimension: $92$
• Newform subspaces: $2$
• Sturm bound: $270$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	405.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(270\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(405, [\chi])\).

	Total	New	Old
Modular forms	228	100	128
Cusp forms	204	92	112
Eisenstein series	24	8	16

Trace form

92 * q + 708 * q^4 - 164 * q^10 + 5188 * q^16 - 8 * q^19 + 968 * q^25 + 2224 * q^31 + 3104 * q^34 - 2908 * q^40 + 1556 * q^46 - 18496 * q^49 + 7140 * q^55 + 2356 * q^61 + 34772 * q^64 + 24 * q^70 - 47472 * q^76 + 12040 * q^79 - 12536 * q^85 + 10104 * q^91 - 24076 * q^94

Decomposition of \(S_{5}^{\mathrm{new}}(405, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
405.5.d.a	$405$	$5$	405.d	15.d	$2$	$44$	$44$	$41.865$		None					45.5.h.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
405.5.d.b	$405$	$5$	405.d	15.d	$2$	$48$	$48$	$41.865$		None		✓	✓		405.5.d.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{5}^{\mathrm{old}}(405, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(405, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)