Space of modular forms of level 2178, weight 2, and Character 2178.i

• Label: 2178.2.i
• Level: $2178$
• Weight: $2$
• Character orbit: 2178.i
• Rep. character: $\chi_{2178}(725,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $216$
• Sturm bound: $792$

Defining parameters

Level:	\( N \)	\(=\)	\( 2178 = 2 \cdot 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2178.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 99 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(792\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2178, [\chi])\).

	Total	New	Old
Modular forms	840	216	624
Cusp forms	744	216	528
Eisenstein series	96	0	96

Trace form

216 * q - 6 * q^3 - 108 * q^4 - 12 * q^5 + 22 * q^9 - 20 * q^15 - 108 * q^16 + 12 * q^20 + 36 * q^23 + 96 * q^25 + 12 * q^31 + 6 * q^34 - 14 * q^36 - 24 * q^37 + 30 * q^38 - 24 * q^42 - 20 * q^45 + 12 * q^47 + 6 * q^48 + 108 * q^49 - 12 * q^58 - 6 * q^59 - 8 * q^60 + 216 * q^64 + 6 * q^67 + 68 * q^69 + 12 * q^70 - 6 * q^75 + 16 * q^78 - 2 * q^81 + 12 * q^82 - 90 * q^86 + 48 * q^91 - 36 * q^92 - 60 * q^93 - 6 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(2178, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2178, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2178, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1089, [\chi])\)\(^{\oplus 2}\)