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Properties

Label 2178.2.z
Level $2178$
Weight $2$
Character orbit 2178.z
Rep. character $\chi_{2178}(17,\cdot)$
Character field $\Q(\zeta_{110})$
Dimension $1760$
Sturm bound $792$

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Defining parameters

Level: \( N \) \(=\) \( 2178 = 2 \cdot 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2178.z (of order \(110\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 363 \)
Character field: \(\Q(\zeta_{110})\)
Sturm bound: \(792\)

Dimensions

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

Total New Old
Modular forms 16160 1760 14400
Cusp forms 15520 1760 13760
Eisenstein series 640 0 640

Trace form

\( 1760 q + 44 q^{4} + O(q^{10}) \) \( 1760 q + 44 q^{4} + 44 q^{10} + 88 q^{13} + 44 q^{16} - 76 q^{22} - 52 q^{25} + 20 q^{28} + 116 q^{31} - 16 q^{34} + 8 q^{37} + 20 q^{40} - 40 q^{46} - 220 q^{49} - 40 q^{52} - 144 q^{55} + 60 q^{58} - 40 q^{61} + 44 q^{64} + 48 q^{67} - 92 q^{70} + 108 q^{73} - 136 q^{79} + 72 q^{82} + 12 q^{88} + 16 q^{91} + 40 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{2}^{\mathrm{old}}(2178, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(726, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1089, [\chi])\)\(^{\oplus 2}\)