↑

Properties

Label 1248.2.ch
Level $1248$
Weight $2$
Character orbit 1248.ch
Rep. character $\chi_{1248}(499,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $448$
Sturm bound $448$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1248.ch (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 416 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1248, [\chi])\).

Total New Old
Modular forms 912 448 464
Cusp forms 880 448 432
Eisenstein series 32 0 32

Trace form

\( 448 q + O(q^{10}) \) \( 448 q - 64 q^{14} + 32 q^{20} + 16 q^{22} - 64 q^{28} + 16 q^{30} + 80 q^{32} - 40 q^{34} + 32 q^{43} - 32 q^{44} + 72 q^{46} - 448 q^{49} - 40 q^{50} + 32 q^{55} - 64 q^{59} + 48 q^{60} - 144 q^{62} + 48 q^{68} + 56 q^{70} - 128 q^{71} + 96 q^{76} - 80 q^{83} - 96 q^{86} - 16 q^{88} + 16 q^{90} - 48 q^{91} + 48 q^{94} - 72 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1248, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1248, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1248, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 2}\)