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

• Label: 1008.3.el
• Level: $1008$
• Weight: $3$
• Character orbit: 1008.el
• Rep. character: $\chi_{1008}(221,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $1520$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1008.el (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1008 \)
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	1552	0
Cusp forms	1520	1520	0
Eisenstein series	32	32	0

Trace form

1520 * q - 6 * q^2 - 2 * q^3 + 2 * q^4 - 8 * q^6 - 4 * q^10 - 2 * q^12 - 4 * q^13 - 6 * q^14 - 16 * q^15 + 2 * q^16 + 114 * q^18 - 4 * q^19 - 12 * q^20 + 32 * q^21 - 4 * q^22 + 138 * q^24 - 8 * q^27 + 24 * q^28 - 12 * q^29 - 58 * q^30 + 4 * q^31 - 6 * q^32 - 4 * q^33 - 12 * q^34 - 150 * q^35 - 76 * q^36 - 4 * q^37 - 4 * q^40 - 286 * q^42 - 4 * q^43 + 198 * q^44 - 202 * q^45 - 20 * q^46 - 12 * q^47 - 288 * q^48 - 4 * q^49 - 12 * q^50 - 198 * q^51 - 4 * q^52 - 590 * q^54 - 300 * q^56 - 4 * q^58 - 6 * q^59 + 142 * q^60 + 2 * q^61 - 204 * q^63 - 16 * q^64 - 12 * q^65 + 422 * q^66 + 2 * q^67 - 26 * q^69 + 96 * q^70 - 158 * q^72 + 120 * q^75 - 4 * q^76 - 6 * q^77 - 54 * q^78 + 4 * q^79 - 4 * q^81 + 4 * q^82 + 708 * q^83 - 28 * q^84 - 54 * q^85 - 4 * q^88 - 152 * q^90 - 204 * q^91 - 12 * q^92 + 34 * q^93 - 30 * q^94 - 12 * q^95 - 540 * q^96 - 8 * q^97 - 330 * q^98 - 170 * 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.