Properties

Label 32.3.h
Level $32$
Weight $3$
Character orbit 32.h
Rep. character $\chi_{32}(3,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $28$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 32.h (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(32, [\chi])\).

Total New Old
Modular forms 36 36 0
Cusp forms 28 28 0
Eisenstein series 8 8 0

Trace form

\( 28q - 4q^{2} - 4q^{3} - 4q^{4} - 4q^{5} - 4q^{6} - 4q^{7} - 4q^{8} - 4q^{9} + O(q^{10}) \) \( 28q - 4q^{2} - 4q^{3} - 4q^{4} - 4q^{5} - 4q^{6} - 4q^{7} - 4q^{8} - 4q^{9} - 44q^{10} - 4q^{11} - 52q^{12} - 4q^{13} - 20q^{14} - 8q^{15} + 16q^{16} + 56q^{18} - 4q^{19} + 76q^{20} - 4q^{21} + 144q^{22} - 68q^{23} + 208q^{24} - 4q^{25} + 96q^{26} - 100q^{27} + 56q^{28} - 4q^{29} + 20q^{30} - 24q^{32} - 8q^{33} - 48q^{34} + 92q^{35} - 336q^{36} - 4q^{37} - 396q^{38} + 188q^{39} - 408q^{40} - 4q^{41} - 424q^{42} + 92q^{43} - 188q^{44} - 40q^{45} - 36q^{46} - 8q^{47} + 48q^{48} + 308q^{50} + 224q^{51} + 420q^{52} - 164q^{53} + 592q^{54} + 252q^{55} + 552q^{56} - 4q^{57} + 528q^{58} + 124q^{59} + 440q^{60} - 68q^{61} + 216q^{62} - 232q^{64} - 8q^{65} - 580q^{66} - 164q^{67} - 368q^{68} + 188q^{69} - 664q^{70} - 260q^{71} - 748q^{72} - 4q^{73} - 532q^{74} - 488q^{75} - 516q^{76} + 220q^{77} - 236q^{78} - 520q^{79} + 312q^{80} + 636q^{82} - 484q^{83} + 992q^{84} + 96q^{85} + 688q^{86} - 452q^{87} + 672q^{88} - 4q^{89} + 872q^{90} - 196q^{91} + 616q^{92} + 32q^{93} + 40q^{94} - 128q^{96} - 8q^{97} - 328q^{98} + 216q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(32, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
32.3.h.a \(28\) \(0.872\) None \(-4\) \(-4\) \(-4\) \(-4\)