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

• Label: 2178.2.w
• Level: $2178$
• Weight: $2$
• Character orbit: 2178.w
• Rep. character: $\chi_{2178}(65,\cdot)$
• Character field: $\Q(\zeta_{66})$
• Dimension: $2640$
• Sturm bound: $792$

Defining parameters

Level:	\( N \)	\(=\)	\( 2178 = 2 \cdot 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2178.w (of order \(66\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1089 \)
Character field:			\(\Q(\zeta_{66})\)
Sturm bound:			\(792\)

Dimensions

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

	Total	New	Old
Modular forms	8000	2640	5360
Cusp forms	7840	2640	5200
Eisenstein series	160	0	160

Trace form

2640 * q - 2 * q^3 + 132 * q^4 + 18 * q^9 - 15 * q^11 - 18 * q^12 + 36 * q^15 + 132 * q^16 + 3 * q^22 + 36 * q^23 - 132 * q^25 - 8 * q^27 + 23 * q^33 + 6 * q^34 - 6 * q^36 - 168 * q^38 - 24 * q^42 - 20 * q^45 - 2 * q^48 - 132 * q^49 - 198 * q^51 + 12 * q^55 - 11 * q^57 - 12 * q^58 - 18 * q^59 - 8 * q^60 - 110 * q^63 - 264 * q^64 - 11 * q^66 - 6 * q^67 + 84 * q^69 + 12 * q^70 + 42 * q^75 - 33 * q^76 - 66 * q^77 - 16 * q^78 - 6 * q^81 + 12 * q^82 + 132 * q^85 - 42 * q^86 - 30 * q^88 - 176 * q^90 - 216 * q^91 + 162 * q^92 + 26 * q^93 - 528 * q^95 + 6 * q^97 - 58 * q^99

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

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