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Properties

Label 2850.2.k
Level $2850$
Weight $2$
Character orbit 2850.k
Rep. character $\chi_{2850}(2243,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $216$
Sturm bound $1200$

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Defining parameters

Level: \( N \) \(=\) \( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2850.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(1200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2850, [\chi])\).

Total New Old
Modular forms 1248 216 1032
Cusp forms 1152 216 936
Eisenstein series 96 0 96

Trace form

\( 216 q - 8 q^{3} - 16 q^{6} - 8 q^{7} + O(q^{10}) \) \( 216 q - 8 q^{3} - 16 q^{6} - 8 q^{7} + 8 q^{12} - 16 q^{13} - 216 q^{16} + 32 q^{21} + 8 q^{22} + 16 q^{27} - 8 q^{28} + 32 q^{31} - 32 q^{33} - 16 q^{36} + 32 q^{37} - 24 q^{42} + 32 q^{43} + 64 q^{46} + 8 q^{48} + 16 q^{52} - 40 q^{58} - 160 q^{61} - 16 q^{63} - 80 q^{67} + 24 q^{73} + 40 q^{78} - 128 q^{81} - 32 q^{82} + 8 q^{88} - 128 q^{91} + 56 q^{93} + 16 q^{96} + 56 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2850, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1425, [\chi])\)\(^{\oplus 2}\)