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Properties

Label 2496.2.fi
Level $2496$
Weight $2$
Character orbit 2496.fi
Rep. character $\chi_{2496}(19,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $3584$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2496.fi (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 832 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2496, [\chi])\).

Total New Old
Modular forms 7232 3584 3648
Cusp forms 7104 3584 3520
Eisenstein series 128 0 128

Trace form

\( 3584 q + O(q^{10}) \) \( 3584 q - 64 q^{12} + 64 q^{20} + 160 q^{28} + 80 q^{32} - 80 q^{34} + 64 q^{46} + 128 q^{52} + 64 q^{55} - 128 q^{59} - 96 q^{60} - 96 q^{68} - 48 q^{70} - 128 q^{71} + 128 q^{76} + 128 q^{86} - 80 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2496, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2496, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2496, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(832, [\chi])\)\(^{\oplus 2}\)