↑

Properties

Label 3283.2.bb
Level $3283$
Weight $2$
Character orbit 3283.bb
Rep. character $\chi_{3283}(135,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $3696$
Sturm bound $634$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3283 = 7^{2} \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3283.bb (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(634\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3283, [\chi])\).

Total New Old
Modular forms 3840 3696 144
Cusp forms 3792 3696 96
Eisenstein series 48 0 48

Trace form

\( 3696 q + 308 q^{4} - 2 q^{5} - 8 q^{6} + 6 q^{7} + 308 q^{9} + O(q^{10}) \) \( 3696 q + 308 q^{4} - 2 q^{5} - 8 q^{6} + 6 q^{7} + 308 q^{9} - 20 q^{11} - 80 q^{12} - 72 q^{14} - 8 q^{15} + 300 q^{16} - 8 q^{17} - 18 q^{18} - 52 q^{19} - 24 q^{20} + 2 q^{21} - 20 q^{22} - 56 q^{23} + 32 q^{24} + 294 q^{25} - 22 q^{26} - 30 q^{27} + 6 q^{28} - 12 q^{30} - 4 q^{31} - 20 q^{32} - 10 q^{33} - 24 q^{34} - 46 q^{35} - 576 q^{36} - 8 q^{37} - 10 q^{39} + 148 q^{40} + 36 q^{41} + 90 q^{42} + 20 q^{43} + 62 q^{44} + 74 q^{45} - 34 q^{46} + 18 q^{47} + 4 q^{48} - 18 q^{49} - 216 q^{50} - 38 q^{51} + 22 q^{52} - 88 q^{53} + 22 q^{54} - 12 q^{55} + 12 q^{56} - 10 q^{57} - 38 q^{58} - 22 q^{59} - 112 q^{60} - 2 q^{61} - 8 q^{62} - 14 q^{63} - 648 q^{64} - 12 q^{65} - 324 q^{66} - 144 q^{68} - 144 q^{69} - 150 q^{70} - 66 q^{71} - 66 q^{72} - 26 q^{73} - 68 q^{74} - 262 q^{75} - 84 q^{76} - 68 q^{77} - 68 q^{78} - 22 q^{79} - 54 q^{80} + 412 q^{81} - 38 q^{82} - 30 q^{83} + 146 q^{84} + 84 q^{85} + 148 q^{86} + 124 q^{87} - 36 q^{88} + 42 q^{89} + 16 q^{90} + 14 q^{91} + 24 q^{92} + 282 q^{93} - 304 q^{94} - 26 q^{95} - 70 q^{96} + 36 q^{97} + 186 q^{98} - 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3283, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3283, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3283, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)