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Properties

Label 2415.2.bp
Level $2415$
Weight $2$
Character orbit 2415.bp
Rep. character $\chi_{2415}(208,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $704$
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.bp (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 1568 704 864
Cusp forms 1504 704 800
Eisenstein series 64 0 64

Trace form

\( 704 q - 8 q^{7} + 48 q^{8} + O(q^{10}) \) \( 704 q - 8 q^{7} + 48 q^{8} + 24 q^{10} + 16 q^{15} + 384 q^{16} + 16 q^{21} - 16 q^{22} + 48 q^{28} - 24 q^{31} - 48 q^{32} + 72 q^{33} - 96 q^{35} - 704 q^{36} - 24 q^{37} + 72 q^{38} - 144 q^{40} + 8 q^{42} + 144 q^{47} + 64 q^{53} + 24 q^{58} + 48 q^{61} - 16 q^{63} + 56 q^{65} - 144 q^{66} + 16 q^{67} - 264 q^{68} - 40 q^{70} + 48 q^{71} - 24 q^{72} - 48 q^{73} + 48 q^{77} - 128 q^{78} + 352 q^{81} + 64 q^{85} - 64 q^{86} - 24 q^{87} + 16 q^{88} + 48 q^{91} + 80 q^{95} + 64 q^{98} + O(q^{100}) \)

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

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