Properties

Label 75.3.h
Level $75$
Weight $3$
Character orbit 75.h
Rep. character $\chi_{75}(14,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $72$
Newform subspaces $1$
Sturm bound $30$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 75.h (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(30\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(75, [\chi])\).

Total New Old
Modular forms 88 88 0
Cusp forms 72 72 0
Eisenstein series 16 16 0

Trace form

\( 72q - 5q^{3} - 38q^{4} + 5q^{6} - 13q^{9} + O(q^{10}) \) \( 72q - 5q^{3} - 38q^{4} + 5q^{6} - 13q^{9} - 20q^{10} - 45q^{12} - 10q^{13} - 15q^{15} + 22q^{16} - 36q^{19} + 54q^{21} - 50q^{22} - 20q^{24} - 100q^{25} + 100q^{27} + 270q^{28} - 5q^{30} - 126q^{31} + 20q^{33} + 210q^{34} - 213q^{36} + 110q^{37} - 191q^{39} + 140q^{40} - 175q^{42} - 405q^{45} - 210q^{46} + 150q^{48} - 224q^{49} - 60q^{51} - 320q^{52} + 320q^{54} - 10q^{55} - 70q^{58} + 1190q^{60} + 294q^{61} + 795q^{63} + 362q^{64} - 470q^{66} - 260q^{67} + 335q^{69} + 1200q^{70} + 215q^{72} - 150q^{73} + 200q^{75} - 16q^{76} - 1295q^{78} - 346q^{79} + 507q^{81} - 456q^{84} - 1450q^{85} - 430q^{87} - 1710q^{88} - 820q^{90} + 538q^{91} - 560q^{94} + 740q^{96} - 150q^{97} + 60q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(75, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
75.3.h.a \(72\) \(2.044\) None \(0\) \(-5\) \(0\) \(0\)