↑

Properties

Label 3344.2.u
Level $3344$
Weight $2$
Character orbit 3344.u
Rep. character $\chi_{3344}(837,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $720$
Sturm bound $960$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3344 = 2^{4} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3344.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3344, [\chi])\).

Total New Old
Modular forms 968 720 248
Cusp forms 952 720 232
Eisenstein series 16 0 16

Trace form

\( 720 q + 24 q^{6} + O(q^{10}) \) \( 720 q + 24 q^{6} + 24 q^{12} - 16 q^{14} + 40 q^{18} - 16 q^{20} - 40 q^{24} - 48 q^{27} - 80 q^{30} + 40 q^{32} + 64 q^{34} - 104 q^{36} + 16 q^{40} + 40 q^{42} + 16 q^{44} + 80 q^{47} - 40 q^{48} - 720 q^{49} - 104 q^{50} + 80 q^{51} + 72 q^{52} - 136 q^{58} + 16 q^{59} + 80 q^{60} + 24 q^{62} + 72 q^{64} + 32 q^{65} - 24 q^{68} - 56 q^{70} - 72 q^{72} - 176 q^{78} - 720 q^{81} - 8 q^{82} - 80 q^{83} - 152 q^{84} + 96 q^{86} + 104 q^{90} + 32 q^{91} - 48 q^{92} + 96 q^{93} - 80 q^{96} + 72 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3344, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3344, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3344, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)