Space of modular forms of level 408, weight 4, and Character 408.j

• Label: 408.4.j
• Level: $408$
• Weight: $4$
• Character orbit: 408.j
• Rep. character: $\chi_{408}(35,\cdot)$
• Character field: $\Q$
• Dimension: $192$
• Sturm bound: $288$

Defining parameters

Level:	\( N \)	\(=\)	\( 408 = 2^{3} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	408.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Sturm bound:			\(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(408, [\chi])\).

	Total	New	Old
Modular forms	220	192	28
Cusp forms	212	192	20
Eisenstein series	8	0	8

Trace form

192 * q + 30 * q^6 + 72 * q^10 - 78 * q^12 + 168 * q^16 - 424 * q^18 - 168 * q^22 - 354 * q^24 + 4800 * q^25 + 264 * q^27 - 336 * q^28 + 636 * q^30 + 1528 * q^36 + 1428 * q^40 - 1312 * q^42 - 864 * q^43 - 1620 * q^46 - 2274 * q^48 - 8688 * q^49 - 2712 * q^52 + 2446 * q^54 + 4332 * q^58 + 3116 * q^60 + 1152 * q^64 - 2272 * q^66 + 3264 * q^67 - 4368 * q^70 - 2048 * q^72 - 432 * q^73 + 3304 * q^75 - 3624 * q^76 + 6012 * q^78 - 1232 * q^81 + 4356 * q^82 + 8136 * q^84 + 8100 * q^88 - 3568 * q^90 - 6888 * q^94 - 1850 * q^96 + 96 * q^97 - 5312 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(408, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(408, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(408, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)