Properties

Label 75.2.i
Level 75
Weight 2
Character orbit i
Rep. character \(\chi_{75}(4,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 16
Newforms 1
Sturm bound 20
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 75.i (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Newforms: \( 1 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(75, [\chi])\).

Total New Old
Modular forms 48 16 32
Cusp forms 32 16 16
Eisenstein series 16 0 16

Trace form

\(16q \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut -\mathstrut 12q^{14} \) \(\mathstrut -\mathstrut 10q^{16} \) \(\mathstrut +\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut +\mathstrut 20q^{20} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 30q^{22} \) \(\mathstrut -\mathstrut 20q^{23} \) \(\mathstrut +\mathstrut 24q^{24} \) \(\mathstrut -\mathstrut 10q^{25} \) \(\mathstrut +\mathstrut 12q^{26} \) \(\mathstrut +\mathstrut 30q^{28} \) \(\mathstrut +\mathstrut 16q^{29} \) \(\mathstrut -\mathstrut 20q^{30} \) \(\mathstrut +\mathstrut 6q^{31} \) \(\mathstrut +\mathstrut 10q^{33} \) \(\mathstrut -\mathstrut 36q^{34} \) \(\mathstrut +\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut +\mathstrut 30q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut +\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 10q^{42} \) \(\mathstrut +\mathstrut 26q^{44} \) \(\mathstrut +\mathstrut 16q^{46} \) \(\mathstrut +\mathstrut 40q^{47} \) \(\mathstrut +\mathstrut 20q^{50} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut +\mathstrut 40q^{52} \) \(\mathstrut +\mathstrut 10q^{53} \) \(\mathstrut -\mathstrut 2q^{54} \) \(\mathstrut +\mathstrut 10q^{55} \) \(\mathstrut +\mathstrut 10q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 30q^{60} \) \(\mathstrut -\mathstrut 10q^{62} \) \(\mathstrut -\mathstrut 10q^{63} \) \(\mathstrut +\mathstrut 8q^{64} \) \(\mathstrut -\mathstrut 70q^{65} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut -\mathstrut 40q^{67} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 30q^{70} \) \(\mathstrut -\mathstrut 8q^{71} \) \(\mathstrut -\mathstrut 30q^{72} \) \(\mathstrut -\mathstrut 20q^{73} \) \(\mathstrut -\mathstrut 52q^{74} \) \(\mathstrut -\mathstrut 32q^{76} \) \(\mathstrut -\mathstrut 40q^{77} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut -\mathstrut 4q^{81} \) \(\mathstrut +\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 12q^{84} \) \(\mathstrut -\mathstrut 20q^{85} \) \(\mathstrut -\mathstrut 36q^{86} \) \(\mathstrut +\mathstrut 40q^{87} \) \(\mathstrut -\mathstrut 40q^{88} \) \(\mathstrut +\mathstrut 18q^{89} \) \(\mathstrut +\mathstrut 30q^{90} \) \(\mathstrut +\mathstrut 26q^{91} \) \(\mathstrut +\mathstrut 10q^{92} \) \(\mathstrut -\mathstrut 38q^{94} \) \(\mathstrut -\mathstrut 40q^{95} \) \(\mathstrut -\mathstrut 26q^{96} \) \(\mathstrut +\mathstrut 40q^{97} \) \(\mathstrut +\mathstrut 60q^{98} \) \(\mathstrut -\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(75, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
75.2.i.a \(16\) \(0.599\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(-1-\beta _{2}-\beta _{4}+\beta _{6}-\beta _{7}-\beta _{8}+\cdots)q^{2}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(75, [\chi])\) into lower level spaces

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