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Properties

Label 75.3.k
Level $75$
Weight $3$
Character orbit 75.k
Rep. character $\chi_{75}(13,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $80$
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.k (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{20})\)
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 176 80 96
Cusp forms 144 80 64
Eisenstein series 32 0 32

Trace form

\( 80q + 4q^{2} + 4q^{5} - 4q^{7} - 12q^{8} + O(q^{10}) \) \( 80q + 4q^{2} + 4q^{5} - 4q^{7} - 12q^{8} - 4q^{10} - 24q^{12} + 32q^{13} - 24q^{15} + 80q^{16} - 100q^{17} - 48q^{18} - 100q^{19} - 244q^{20} - 100q^{22} - 96q^{23} - 16q^{25} - 40q^{26} + 196q^{28} + 200q^{29} + 264q^{30} + 636q^{32} + 216q^{33} + 100q^{34} + 260q^{35} - 120q^{36} - 184q^{37} - 564q^{38} - 948q^{40} + 160q^{41} - 12q^{42} - 472q^{43} - 700q^{44} - 36q^{45} - 288q^{47} - 48q^{48} + 16q^{50} + 620q^{52} + 304q^{53} + 604q^{55} + 72q^{57} + 1272q^{58} + 800q^{59} + 84q^{60} - 240q^{61} + 1212q^{62} - 12q^{63} + 100q^{64} + 272q^{65} - 80q^{67} + 104q^{68} - 260q^{70} + 36q^{72} - 116q^{73} - 24q^{75} - 88q^{77} - 120q^{78} + 200q^{79} - 164q^{80} + 180q^{81} - 168q^{82} - 1264q^{83} - 1200q^{84} - 212q^{85} - 876q^{87} - 212q^{88} - 1500q^{89} - 444q^{90} - 1504q^{92} - 648q^{93} - 200q^{94} - 784q^{95} + 60q^{96} - 260q^{97} - 92q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.k.a \(80\) \(2.044\) None \(4\) \(0\) \(4\) \(-4\)

Decomposition of \(S_{3}^{\mathrm{old}}(75, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(75, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)