↑

Properties

Label 2112.2.u
Level $2112$
Weight $2$
Character orbit 2112.u
Rep. character $\chi_{2112}(815,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $160$
Sturm bound $768$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2112 = 2^{6} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2112.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2112, [\chi])\).

Total New Old
Modular forms 800 160 640
Cusp forms 736 160 576
Eisenstein series 64 0 64

Trace form

\( 160 q + O(q^{10}) \) \( 160 q - 16 q^{19} + 24 q^{27} + 48 q^{39} + 160 q^{49} + 40 q^{51} - 32 q^{61} - 56 q^{75} - 32 q^{85} - 112 q^{87} - 48 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2112, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2112, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2112, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1056, [\chi])\)\(^{\oplus 2}\)