Properties

Label 2700.2.r
Level $2700$
Weight $2$
Character orbit 2700.r
Rep. character $\chi_{2700}(251,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $216$
Sturm bound $1080$

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Defining parameters

Level: \( N \) \(=\) \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2700.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2700, [\chi])\).

Total New Old
Modular forms 1152 240 912
Cusp forms 1008 216 792
Eisenstein series 144 24 120

Trace form

\( 216 q - 3 q^{2} + q^{4} + O(q^{10}) \) \( 216 q - 3 q^{2} + q^{4} + 2 q^{13} - 18 q^{14} - 3 q^{16} - 3 q^{22} + 12 q^{28} + 6 q^{29} - 33 q^{32} + q^{34} + 8 q^{37} + 33 q^{38} - 12 q^{41} - 28 q^{46} + 74 q^{49} + 2 q^{52} + 30 q^{56} + 14 q^{58} - 6 q^{61} + 10 q^{64} + 33 q^{68} + 20 q^{73} + 78 q^{74} + 15 q^{76} + 18 q^{77} + 26 q^{82} + 33 q^{86} + 21 q^{88} + 84 q^{92} + 16 q^{94} + 8 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2700, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2700, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2700, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)