Properties

Label 1716.2.r
Level $1716$
Weight $2$
Character orbit 1716.r
Rep. character $\chi_{1716}(395,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $656$
Sturm bound $672$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1716.r (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1716 \)
Character field: \(\Q(i)\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1716, [\chi])\).

Total New Old
Modular forms 688 688 0
Cusp forms 656 656 0
Eisenstein series 32 32 0

Trace form

\( 656 q - 16 q^{9} + O(q^{10}) \) \( 656 q - 16 q^{9} - 16 q^{33} + 32 q^{34} - 16 q^{37} - 12 q^{42} + 32 q^{45} - 4 q^{48} - 32 q^{58} - 52 q^{60} - 44 q^{66} + 80 q^{70} - 16 q^{78} - 16 q^{81} + 48 q^{93} - 16 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1716, [\chi])\) into newform subspaces

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