↑

Properties

Label 3696.2.hd
Level $3696$
Weight $2$
Character orbit 3696.hd
Rep. character $\chi_{3696}(5,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $12160$
Sturm bound $1536$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3696 = 2^{4} \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3696.hd (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3696 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1536\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3696, [\chi])\).

Total New Old
Modular forms 12416 12416 0
Cusp forms 12160 12160 0
Eisenstein series 256 256 0

Trace form

\( 12160 q - 18 q^{3} - 12 q^{4} + O(q^{10}) \) \( 12160 q - 18 q^{3} - 12 q^{4} - 96 q^{10} - 48 q^{12} - 48 q^{15} + 20 q^{16} - 22 q^{18} - 36 q^{19} - 44 q^{21} - 160 q^{22} - 18 q^{24} - 16 q^{28} - 14 q^{30} - 72 q^{31} - 48 q^{33} + 8 q^{36} - 12 q^{37} - 36 q^{40} + 16 q^{42} - 128 q^{43} - 48 q^{45} + 36 q^{46} - 48 q^{49} - 30 q^{51} + 36 q^{52} + 120 q^{54} + 20 q^{58} - 74 q^{60} - 36 q^{61} + 32 q^{63} + 96 q^{64} - 24 q^{66} + 32 q^{67} + 60 q^{70} + 26 q^{72} - 78 q^{75} - 80 q^{78} - 24 q^{79} - 12 q^{81} - 84 q^{82} + 174 q^{84} - 128 q^{85} - 32 q^{88} + 16 q^{91} + 18 q^{93} - 108 q^{94} - 18 q^{96} - 68 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3696, [\chi])\) into newform subspaces

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