Properties

Label 32.4.g
Level $32$
Weight $4$
Character orbit 32.g
Rep. character $\chi_{32}(5,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $44$
Newform subspaces $1$
Sturm bound $16$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 32.g (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(32, [\chi])\).

Total New Old
Modular forms 52 52 0
Cusp forms 44 44 0
Eisenstein series 8 8 0

Trace form

\( 44q - 4q^{2} - 4q^{3} - 4q^{4} - 4q^{5} - 4q^{6} - 4q^{7} - 4q^{8} - 4q^{9} + O(q^{10}) \) \( 44q - 4q^{2} - 4q^{3} - 4q^{4} - 4q^{5} - 4q^{6} - 4q^{7} - 4q^{8} - 4q^{9} + 116q^{10} - 4q^{11} - 52q^{12} - 4q^{13} - 212q^{14} - 304q^{16} - 184q^{18} - 4q^{19} + 76q^{20} - 4q^{21} + 192q^{22} + 324q^{23} - 48q^{24} - 4q^{25} + 16q^{26} - 268q^{27} + 376q^{28} - 4q^{29} + 1188q^{30} - 752q^{31} + 616q^{32} - 8q^{33} + 528q^{34} - 460q^{35} + 1456q^{36} - 4q^{37} + 980q^{38} + 596q^{39} - 536q^{40} - 4q^{41} - 2264q^{42} + 804q^{43} - 2044q^{44} + 104q^{45} - 1444q^{46} - 2448q^{48} - 3564q^{50} - 1384q^{51} - 2524q^{52} + 748q^{53} - 1088q^{54} - 292q^{55} + 1192q^{56} - 4q^{57} + 3200q^{58} + 1372q^{59} + 5752q^{60} - 1828q^{61} + 3384q^{62} + 2512q^{63} + 4952q^{64} - 8q^{65} + 5996q^{66} + 2036q^{67} + 2768q^{68} - 1060q^{69} + 1400q^{70} + 220q^{71} - 1708q^{72} - 4q^{73} - 3476q^{74} - 1712q^{75} - 5124q^{76} + 1900q^{77} - 11916q^{78} - 10312q^{80} - 6404q^{82} + 2436q^{83} - 6560q^{84} + 496q^{85} - 928q^{86} - 1292q^{87} + 1248q^{88} - 4q^{89} + 7400q^{90} - 3604q^{91} + 10152q^{92} - 112q^{93} + 12840q^{94} - 6088q^{95} + 17792q^{96} - 8q^{97} + 11224q^{98} - 5424q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(32, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
32.4.g.a \(44\) \(1.888\) None \(-4\) \(-4\) \(-4\) \(-4\)