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Properties

Label 2415.2.x
Level $2415$
Weight $2$
Character orbit 2415.x
Rep. character $\chi_{2415}(622,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $352$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 2415 = 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2415.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2415, [\chi])\).

Total New Old
Modular forms 784 352 432
Cusp forms 752 352 400
Eisenstein series 32 0 32

Trace form

\( 352 q + 8 q^{7} - 48 q^{8} + O(q^{10}) \) \( 352 q + 8 q^{7} - 48 q^{8} - 16 q^{15} - 288 q^{16} - 16 q^{21} + 16 q^{22} - 48 q^{28} - 96 q^{32} + 24 q^{35} - 352 q^{36} - 48 q^{37} - 8 q^{42} - 64 q^{53} - 96 q^{56} - 8 q^{63} + 16 q^{65} + 128 q^{67} - 32 q^{70} - 144 q^{71} - 48 q^{72} + 24 q^{77} - 16 q^{78} - 352 q^{81} + 32 q^{85} - 32 q^{86} + 176 q^{88} + 144 q^{91} + 64 q^{95} + 104 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2415, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2415, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2415, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)