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Properties

Label 95.2.k
Level $95$
Weight $2$
Character orbit 95.k
Rep. character $\chi_{95}(6,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $36$
Newform subspaces $2$
Sturm bound $20$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 95.k (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 2 \)
Sturm bound: \(20\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(95, [\chi])\).

Total New Old
Modular forms 72 36 36
Cusp forms 48 36 12
Eisenstein series 24 0 24

Trace form

\( 36 q - 6 q^{3} - 6 q^{4} - 12 q^{6} - 18 q^{8} - 18 q^{9} + O(q^{10}) \) \( 36 q - 6 q^{3} - 6 q^{4} - 12 q^{6} - 18 q^{8} - 18 q^{9} - 6 q^{10} - 12 q^{12} - 6 q^{13} + 12 q^{14} + 18 q^{16} + 36 q^{18} - 12 q^{19} - 18 q^{21} + 24 q^{22} + 12 q^{23} + 6 q^{24} - 18 q^{26} - 18 q^{27} - 36 q^{28} + 6 q^{29} - 24 q^{30} + 12 q^{31} + 60 q^{32} - 36 q^{33} + 12 q^{34} - 6 q^{35} + 54 q^{36} - 24 q^{37} - 48 q^{38} + 48 q^{39} - 12 q^{40} - 36 q^{41} + 30 q^{42} - 42 q^{43} + 12 q^{44} + 30 q^{46} + 54 q^{47} - 30 q^{48} + 6 q^{49} - 6 q^{50} - 18 q^{51} - 30 q^{52} + 12 q^{53} - 36 q^{54} - 72 q^{56} + 42 q^{57} + 48 q^{58} + 36 q^{59} + 12 q^{60} - 24 q^{61} - 12 q^{62} + 78 q^{63} + 12 q^{64} - 6 q^{65} + 6 q^{66} - 24 q^{67} + 48 q^{68} + 42 q^{69} + 72 q^{70} + 12 q^{71} - 48 q^{72} + 30 q^{73} - 54 q^{74} + 12 q^{75} - 6 q^{76} - 36 q^{77} + 24 q^{78} - 42 q^{79} + 48 q^{80} + 42 q^{81} - 72 q^{82} + 36 q^{84} + 48 q^{85} + 30 q^{86} - 60 q^{87} + 12 q^{88} - 60 q^{89} - 30 q^{90} + 24 q^{91} - 108 q^{92} - 36 q^{94} - 84 q^{96} - 60 q^{97} + 36 q^{98} - 90 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(95, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
95.2.k.a 95.k 19.e $18$ $0.759$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-3\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\beta _{4}+\beta _{15})q^{2}+(\beta _{5}+\beta _{6}+\beta _{8}+\cdots)q^{3}+\cdots\)
95.2.k.b 95.k 19.e $18$ $0.759$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(3\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{14}q^{2}+(-\beta _{4}+\beta _{6}-\beta _{7}-\beta _{15}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(95, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(95, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)