↑

Properties

Label 1024.2.i
Level $1024$
Weight $2$
Character orbit 1024.i
Rep. character $\chi_{1024}(65,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $224$
Sturm bound $256$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1024 = 2^{10} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1024.i (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(256\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1024, [\chi])\).

Total New Old
Modular forms 1152 288 864
Cusp forms 896 224 672
Eisenstein series 256 64 192

Trace form

\( 224 q + 32 q^{9} + O(q^{10}) \) \( 224 q + 32 q^{9} - 32 q^{17} + 32 q^{25} + 32 q^{41} - 32 q^{49} + 32 q^{57} - 64 q^{65} + 32 q^{73} - 32 q^{81} + 32 q^{89} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1024, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1024, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1024, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(512, [\chi])\)\(^{\oplus 2}\)