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Properties

Label 83.13.d
Level $83$
Weight $13$
Character orbit 83.d
Rep. character $\chi_{83}(2,\cdot)$
Character field $\Q(\zeta_{82})$
Dimension $3320$
Sturm bound $91$

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Defining parameters

Level: \( N \) \(=\) \( 83 \)
Weight: \( k \) \(=\) \( 13 \)
Character orbit: \([\chi]\) \(=\) 83.d (of order \(82\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 83 \)
Character field: \(\Q(\zeta_{82})\)
Sturm bound: \(91\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(83, [\chi])\).

Total New Old
Modular forms 3400 3400 0
Cusp forms 3320 3320 0
Eisenstein series 80 80 0

Trace form

\( 3320 q - 41 q^{2} - 959 q^{3} + 168821 q^{4} - 41 q^{5} - 41 q^{6} - 103959 q^{7} - 41 q^{8} - 16496506 q^{9} + O(q^{10}) \) \( 3320 q - 41 q^{2} - 959 q^{3} + 168821 q^{4} - 41 q^{5} - 41 q^{6} - 103959 q^{7} - 41 q^{8} - 16496506 q^{9} - 1177523 q^{10} - 510447 q^{11} + 9260361 q^{12} - 41 q^{13} - 41 q^{14} - 41 q^{15} - 254123539 q^{16} - 5571759 q^{17} - 41 q^{18} - 41 q^{19} - 41 q^{20} - 178300229 q^{21} - 41 q^{22} - 111355239 q^{23} - 41 q^{24} + 3531291356 q^{25} - 18061835 q^{26} + 79728763 q^{27} + 204811611 q^{28} - 1486960311 q^{29} + 2621683607 q^{30} + 665742969 q^{31} - 41 q^{32} - 75392357 q^{33} - 41 q^{34} - 41 q^{35} + 48406362775 q^{36} + 280627161 q^{37} - 6646145351 q^{38} - 41 q^{39} + 7119722017 q^{40} - 22893748959 q^{41} - 41 q^{42} - 41 q^{43} + 11512674609 q^{44} - 41 q^{45} - 41 q^{46} - 41 q^{47} - 85368259779 q^{48} - 190309256738 q^{49} - 41 q^{50} + 145740933115 q^{51} - 41 q^{52} - 41 q^{53} - 41 q^{54} - 41 q^{55} - 41 q^{56} - 41 q^{57} - 41 q^{58} + 63584241009 q^{59} - 41 q^{60} + 29216180937 q^{61} - 41 q^{62} + 146920039725 q^{63} + 117438103841 q^{64} - 362112989225 q^{65} + 2068916310999 q^{66} - 1100569186121 q^{67} + 1535147843991 q^{68} + 2236977811259 q^{69} + 458922797335 q^{70} - 639644821241 q^{71} - 7978148147241 q^{72} - 934353519881 q^{73} + 815966806999 q^{74} + 5411467503249 q^{75} + 3394295562199 q^{76} + 430911666683 q^{77} - 5667054697461 q^{78} - 3051933731321 q^{79} - 11783900344361 q^{80} - 6466816977352 q^{81} + 888475749620 q^{83} + 20813327672496 q^{84} + 4716077479303 q^{85} + 3271531660321 q^{86} + 1997922071243 q^{87} - 14830205644841 q^{88} - 6897811405001 q^{89} - 21598740430739 q^{90} - 3143189940521 q^{91} + 5397802208961 q^{92} + 17602313349403 q^{93} + 4170880562179 q^{94} + 6134278439335 q^{95} - 5836762624041 q^{96} - 4391492497961 q^{97} - 23832141189161 q^{98} - 9540050822907 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{13}^{\mathrm{new}}(83, [\chi])\) into newform subspaces

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