↑

Properties

Label 75.2.l
Level $75$
Weight $2$
Character orbit 75.l
Rep. character $\chi_{75}(2,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $64$
Newform subspaces $1$
Sturm bound $20$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 75.l (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
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 96 96 0
Cusp forms 64 64 0
Eisenstein series 32 32 0

Trace form

\( 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9} + O(q^{10}) \) \( 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9} - 20 q^{10} - 10 q^{12} - 20 q^{13} - 10 q^{15} - 8 q^{16} - 10 q^{18} - 6 q^{21} + 20 q^{22} + 40 q^{25} - 10 q^{27} + 40 q^{28} - 10 q^{30} - 12 q^{31} - 10 q^{33} + 20 q^{34} - 22 q^{36} - 20 q^{37} + 30 q^{39} - 20 q^{40} + 90 q^{42} - 20 q^{43} + 70 q^{45} - 12 q^{46} + 100 q^{48} - 16 q^{51} + 20 q^{52} + 120 q^{54} - 20 q^{55} + 70 q^{57} - 20 q^{58} + 50 q^{60} - 12 q^{61} - 20 q^{63} - 100 q^{64} - 30 q^{66} - 60 q^{67} - 80 q^{69} - 100 q^{70} - 150 q^{72} - 60 q^{73} - 90 q^{75} - 64 q^{76} - 80 q^{78} - 60 q^{79} + 14 q^{81} - 60 q^{82} - 130 q^{84} + 60 q^{85} - 60 q^{87} + 20 q^{88} - 70 q^{90} - 12 q^{91} - 20 q^{93} + 260 q^{94} + 42 q^{96} + 120 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(75, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
75.2.l.a 75.l 75.l $64$ $0.599$ None \(0\) \(-10\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{20}]$