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Properties

Label 3136.2.cr
Level $3136$
Weight $2$
Character orbit 3136.cr
Rep. character $\chi_{3136}(29,\cdot)$
Character field $\Q(\zeta_{112})$
Dimension $21408$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 3136 = 2^{6} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3136.cr (of order \(112\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3136 \)
Character field: \(\Q(\zeta_{112})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 21600 21600 0
Cusp forms 21408 21408 0
Eisenstein series 192 192 0

Trace form

\( 21408 q - 40 q^{2} - 40 q^{3} - 40 q^{4} - 40 q^{5} - 40 q^{6} - 48 q^{7} - 40 q^{8} - 40 q^{9} + O(q^{10}) \) \( 21408 q - 40 q^{2} - 40 q^{3} - 40 q^{4} - 40 q^{5} - 40 q^{6} - 48 q^{7} - 40 q^{8} - 40 q^{9} - 40 q^{10} - 40 q^{11} - 40 q^{12} - 40 q^{13} - 48 q^{14} - 40 q^{15} - 40 q^{16} - 40 q^{17} - 96 q^{18} - 96 q^{19} - 40 q^{20} - 48 q^{21} - 40 q^{22} - 40 q^{23} - 120 q^{24} - 40 q^{25} - 40 q^{26} - 40 q^{27} - 88 q^{28} - 40 q^{29} - 96 q^{30} - 40 q^{32} - 40 q^{34} - 48 q^{35} - 40 q^{36} - 40 q^{37} - 120 q^{38} - 40 q^{39} - 40 q^{40} - 40 q^{41} - 88 q^{42} - 40 q^{43} - 40 q^{44} - 40 q^{45} - 40 q^{46} - 40 q^{47} - 96 q^{48} - 48 q^{49} - 48 q^{50} - 40 q^{51} + 56 q^{52} - 40 q^{53} - 40 q^{54} - 40 q^{55} - 48 q^{56} - 40 q^{57} - 40 q^{58} - 168 q^{59} - 40 q^{60} - 40 q^{61} + 40 q^{62} - 96 q^{63} + 152 q^{64} - 80 q^{65} + 120 q^{66} - 96 q^{67} - 96 q^{68} - 40 q^{69} - 48 q^{70} + 280 q^{71} - 40 q^{72} - 40 q^{73} - 40 q^{74} - 40 q^{75} - 40 q^{76} - 48 q^{77} + 56 q^{78} - 96 q^{79} - 384 q^{80} - 40 q^{81} + 360 q^{82} - 40 q^{83} - 160 q^{84} - 40 q^{85} - 40 q^{86} - 40 q^{87} - 40 q^{88} - 40 q^{89} - 328 q^{90} - 48 q^{91} - 40 q^{92} + 80 q^{93} - 40 q^{94} + 640 q^{96} - 184 q^{98} - 144 q^{99} + O(q^{100}) \)

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.