Space of modular forms of level 1176, weight 2, and Character 1176.bc

• Label: 1176.2.bc
• Level: $1176$
• Weight: $2$
• Character orbit: 1176.bc
• Rep. character: $\chi_{1176}(373,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $160$
• Sturm bound: $448$

Defining parameters

Level:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1176.bc (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1176, [\chi])\).

	Total	New	Old
Modular forms	480	160	320
Cusp forms	416	160	256
Eisenstein series	64	0	64

Trace form

160 * q - 4 * q^2 + 4 * q^4 + 20 * q^8 + 80 * q^9 - 6 * q^10 + 12 * q^16 + 4 * q^18 + 40 * q^20 + 12 * q^22 + 16 * q^23 + 6 * q^24 + 80 * q^25 - 6 * q^26 + 8 * q^30 + 24 * q^31 + 6 * q^32 + 24 * q^34 + 8 * q^36 + 26 * q^38 + 6 * q^40 - 32 * q^44 - 32 * q^46 + 24 * q^47 + 16 * q^48 - 80 * q^50 - 44 * q^52 + 64 * q^55 + 16 * q^57 - 46 * q^58 + 34 * q^60 - 100 * q^62 + 16 * q^64 - 12 * q^66 - 16 * q^68 + 96 * q^71 + 10 * q^72 - 8 * q^73 + 2 * q^74 + 32 * q^76 - 36 * q^78 - 16 * q^79 + 56 * q^80 - 80 * q^81 - 74 * q^86 - 24 * q^87 + 22 * q^88 - 12 * q^90 + 96 * q^92 + 48 * q^94 - 24 * q^95 - 10 * q^96 + 48 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(1176, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1176, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1176, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 2}\)