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Properties

Label 2075.2.e
Level $2075$
Weight $2$
Character orbit 2075.e
Rep. character $\chi_{2075}(82,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $248$
Sturm bound $420$

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Defining parameters

Level: \( N \) \(=\) \( 2075 = 5^{2} \cdot 83 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2075.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 415 \)
Character field: \(\Q(i)\)
Sturm bound: \(420\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2075, [\chi])\).

Total New Old
Modular forms 432 256 176
Cusp forms 408 248 160
Eisenstein series 24 8 16

Trace form

\( 248 q + 4 q^{3} + 8 q^{7} + O(q^{10}) \) \( 248 q + 4 q^{3} + 8 q^{7} - 24 q^{11} - 32 q^{12} - 260 q^{16} + 8 q^{21} - 4 q^{23} + 24 q^{26} - 8 q^{27} + 4 q^{28} + 8 q^{31} + 40 q^{33} - 156 q^{36} + 16 q^{37} + 56 q^{38} - 8 q^{41} - 20 q^{48} + 96 q^{51} + 104 q^{61} + 44 q^{63} - 64 q^{68} - 24 q^{77} - 132 q^{78} - 384 q^{81} + 28 q^{83} + 16 q^{86} + 28 q^{87} + 84 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2075, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2075, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2075, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(415, [\chi])\)\(^{\oplus 2}\)