Space of modular forms of level 1976, weight 2, and Character 1976.fu

• Label: 1976.2.fu
• Level: $1976$
• Weight: $2$
• Character orbit: 1976.fu
• Rep. character: $\chi_{1976}(547,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $1440$
• Sturm bound: $560$

Defining parameters

Level:	\( N \)	\(=\)	\( 1976 = 2^{3} \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1976.fu (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q(\zeta_{18})\)
Sturm bound:			\(560\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1976, [\chi])\).

	Total	New	Old
Modular forms	1704	1440	264
Cusp forms	1656	1440	216
Eisenstein series	48	0	48

Trace form

1440 * q + 12 * q^4 - 12 * q^6 - 6 * q^10 + 18 * q^14 - 12 * q^16 + 42 * q^24 + 36 * q^28 - 42 * q^30 - 48 * q^34 + 12 * q^36 - 66 * q^38 + 84 * q^40 + 24 * q^41 - 126 * q^42 - 66 * q^44 + 150 * q^48 + 720 * q^49 - 54 * q^50 - 48 * q^51 + 114 * q^54 - 66 * q^60 - 42 * q^62 - 66 * q^64 - 30 * q^66 - 24 * q^68 - 144 * q^70 - 180 * q^72 - 42 * q^74 - 72 * q^76 + 30 * q^78 - 18 * q^80 - 24 * q^81 - 120 * q^82 - 216 * q^84 - 144 * q^86 - 186 * q^90 + 60 * q^92 + 204 * q^96 + 174 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(1976, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1976, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1976, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)