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

• Label: 405.4.r
• Level: $405$
• Weight: $4$
• Character orbit: 405.r
• Rep. character: $\chi_{405}(8,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $624$
• Sturm bound: $216$

Defining parameters

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 135 \)
Character field:			\(\Q(\zeta_{36})\)
Sturm bound:			\(216\)

Dimensions

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

	Total	New	Old
Modular forms	2016	672	1344
Cusp forms	1872	624	1248
Eisenstein series	144	48	96

Trace form

624 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 756 * q^20 - 12 * q^22 + 324 * q^23 + 420 * q^25 - 24 * q^28 - 24 * q^31 - 1752 * q^32 - 2466 * q^35 - 6 * q^37 + 132 * q^38 - 396 * q^40 - 1680 * q^41 - 12 * q^43 - 12 * q^46 + 3480 * q^47 + 684 * q^50 + 84 * q^52 - 24 * q^55 + 4752 * q^56 - 12 * q^58 - 132 * q^61 + 18 * q^62 - 2076 * q^65 + 3660 * q^67 - 2676 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 792 * q^76 + 3324 * q^77 - 24 * q^82 + 2832 * q^83 - 12 * q^85 + 12516 * q^86 - 3036 * q^88 - 12 * q^91 + 1938 * q^92 + 4302 * q^95 + 6900 * q^97 + 5832 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(405, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

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

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