Space of modular forms of level 1008, weight 3, and Character 1008.en

• Label: 1008.3.en
• Level: $1008$
• Weight: $3$
• Character orbit: 1008.en
• Rep. character: $\chi_{1008}(43,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $1152$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1008.en (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 144 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1008, [\chi])\).

	Total	New	Old
Modular forms	1552	1152	400
Cusp forms	1520	1152	368
Eisenstein series	32	0	32

Trace form

1152 * q - 12 * q^6 - 120 * q^12 + 84 * q^20 + 32 * q^24 + 192 * q^26 + 96 * q^27 + 216 * q^30 + 32 * q^36 + 504 * q^38 - 384 * q^39 - 336 * q^46 - 52 * q^48 - 4032 * q^49 + 156 * q^50 - 180 * q^58 - 288 * q^59 + 76 * q^60 - 360 * q^62 - 504 * q^64 - 232 * q^66 + 156 * q^68 + 364 * q^72 - 84 * q^74 + 448 * q^75 - 312 * q^76 - 524 * q^78 - 1200 * q^80 + 792 * q^82 + 636 * q^86 + 896 * q^87 + 48 * q^88 - 1336 * q^90 - 228 * q^92 - 96 * q^93 - 544 * q^96 - 256 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1008, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)