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Properties

Label 3136.2.db
Level $3136$
Weight $2$
Character orbit 3136.db
Rep. character $\chi_{3136}(3,\cdot)$
Character field $\Q(\zeta_{336})$
Dimension $42816$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 3136 = 2^{6} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3136.db (of order \(336\) and degree \(96\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3136 \)
Character field: \(\Q(\zeta_{336})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3136, [\chi])\).

Total New Old
Modular forms 43200 43200 0
Cusp forms 42816 42816 0
Eisenstein series 384 384 0

Trace form

\( 42816 q - 104 q^{2} - 88 q^{3} - 104 q^{4} - 88 q^{5} - 112 q^{6} - 96 q^{7} - 80 q^{8} - 104 q^{9} + O(q^{10}) \) \( 42816 q - 104 q^{2} - 88 q^{3} - 104 q^{4} - 88 q^{5} - 112 q^{6} - 96 q^{7} - 80 q^{8} - 104 q^{9} - 88 q^{10} - 104 q^{11} - 88 q^{12} - 112 q^{13} - 96 q^{14} - 80 q^{15} - 104 q^{16} - 88 q^{17} - 48 q^{18} - 144 q^{19} - 112 q^{20} - 96 q^{21} - 80 q^{22} - 104 q^{23} - 88 q^{24} - 104 q^{25} - 88 q^{26} - 112 q^{27} - 56 q^{28} - 80 q^{29} - 48 q^{30} - 288 q^{31} - 104 q^{32} - 112 q^{34} - 96 q^{35} - 80 q^{36} - 104 q^{37} - 88 q^{38} - 104 q^{39} - 88 q^{40} - 112 q^{41} - 56 q^{42} - 80 q^{43} - 104 q^{44} - 88 q^{45} - 104 q^{46} - 88 q^{47} - 96 q^{49} - 144 q^{50} - 104 q^{51} - 232 q^{52} - 104 q^{53} - 88 q^{54} - 112 q^{55} - 96 q^{56} - 80 q^{57} - 104 q^{58} + 104 q^{59} - 104 q^{60} - 88 q^{61} - 224 q^{62} + 112 q^{64} - 208 q^{65} - 376 q^{66} - 48 q^{67} - 144 q^{68} - 112 q^{69} - 96 q^{70} + 240 q^{71} - 104 q^{72} - 88 q^{73} - 104 q^{74} - 88 q^{75} - 112 q^{76} - 96 q^{77} + 16 q^{78} - 48 q^{79} + 288 q^{80} - 104 q^{81} - 408 q^{82} - 112 q^{83} - 208 q^{84} - 80 q^{85} - 104 q^{86} - 88 q^{87} - 104 q^{88} - 88 q^{89} - 112 q^{90} - 96 q^{91} - 80 q^{92} - 224 q^{93} - 88 q^{94} - 208 q^{95} - 1584 q^{96} - 232 q^{98} - 240 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3136, [\chi])\) into newform subspaces

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