↑

Properties

Label 3648.2.r
Level $3648$
Weight $2$
Character orbit 3648.r
Rep. character $\chi_{3648}(113,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $312$
Sturm bound $1280$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3648 = 2^{6} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3648.r (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 912 \)
Character field: \(\Q(i)\)
Sturm bound: \(1280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3648, [\chi])\).

Total New Old
Modular forms 1312 328 984
Cusp forms 1248 312 936
Eisenstein series 64 16 48

Trace form

\( 312 q + O(q^{10}) \) \( 312 q + 12 q^{19} + 8 q^{43} - 24 q^{45} - 280 q^{49} - 40 q^{61} - 48 q^{63} - 8 q^{81} + 8 q^{93} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3648, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3648, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3648, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1824, [\chi])\)\(^{\oplus 2}\)