↑

Properties

Label 1024.2.k
Level $1024$
Weight $2$
Character orbit 1024.k
Rep. character $\chi_{1024}(33,\cdot)$
Character field $\Q(\zeta_{32})$
Dimension $480$
Sturm bound $256$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1024 = 2^{10} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1024.k (of order \(32\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 128 \)
Character field: \(\Q(\zeta_{32})\)
Sturm bound: \(256\)

Dimensions

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

Total New Old
Modular forms 2176 544 1632
Cusp forms 1920 480 1440
Eisenstein series 256 64 192

Trace form

\( 480 q + 32 q^{5} - 32 q^{9} + O(q^{10}) \) \( 480 q + 32 q^{5} - 32 q^{9} + 32 q^{13} - 32 q^{17} + 32 q^{21} - 32 q^{25} + 32 q^{29} - 32 q^{33} + 32 q^{37} - 32 q^{41} + 32 q^{45} - 32 q^{49} + 32 q^{53} - 32 q^{57} + 32 q^{61} + 32 q^{69} - 32 q^{73} + 32 q^{77} - 32 q^{81} + 32 q^{85} - 32 q^{89} + 32 q^{93} - 32 q^{97} + O(q^{100}) \)

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

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