Space of modular forms of level 1176, weight 3, and Character 1176.bq

• Label: 1176.3.bq
• Level: $1176$
• Weight: $3$
• Character orbit: 1176.bq
• Rep. character: $\chi_{1176}(43,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $1344$
• Sturm bound: $672$

Defining parameters

Level:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1176.bq (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 392 \)
Character field:			\(\Q(\zeta_{14})\)
Sturm bound:			\(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1176, [\chi])\).

	Total	New	Old
Modular forms	2712	1344	1368
Cusp forms	2664	1344	1320
Eisenstein series	48	0	48

Trace form

1344 * q - 12 * q^8 - 672 * q^9 - 36 * q^10 - 22 * q^14 - 48 * q^16 - 164 * q^20 + 12 * q^22 + 90 * q^24 + 1120 * q^25 + 92 * q^26 + 272 * q^28 + 48 * q^30 + 100 * q^32 + 244 * q^34 - 96 * q^35 - 8 * q^38 - 300 * q^40 - 84 * q^42 - 440 * q^44 + 80 * q^46 - 144 * q^48 + 16 * q^49 + 372 * q^50 + 100 * q^52 + 70 * q^56 + 96 * q^57 - 260 * q^58 + 256 * q^59 + 180 * q^60 - 392 * q^62 + 312 * q^64 - 72 * q^66 + 576 * q^67 - 412 * q^68 - 710 * q^70 + 90 * q^72 - 160 * q^73 + 220 * q^74 + 234 * q^76 - 180 * q^78 + 1136 * q^80 - 2016 * q^81 - 1340 * q^82 + 24 * q^84 - 484 * q^86 + 1068 * q^88 - 108 * q^90 - 960 * q^91 - 502 * q^92 + 618 * q^94 + 300 * q^96 - 256 * q^97 + 712 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(1176, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1176, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1176, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 2}\)