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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
75.3.h.a 75.h 75.h $72$ $2.044$ None \(0\) \(-5\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$