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Properties

Label 95.2.e
Level $95$
Weight $2$
Character orbit 95.e
Rep. character $\chi_{95}(11,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
Newform subspaces $3$
Sturm bound $20$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 95.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
Sturm bound: \(20\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 24 16 8
Cusp forms 16 16 0
Eisenstein series 8 0 8

Trace form

\( 16 q - 2 q^{2} - 2 q^{3} - 10 q^{4} + 4 q^{6} - 12 q^{7} + 12 q^{8} - 6 q^{9} + O(q^{10}) \) \( 16 q - 2 q^{2} - 2 q^{3} - 10 q^{4} + 4 q^{6} - 12 q^{7} + 12 q^{8} - 6 q^{9} - 8 q^{11} + 12 q^{12} + 6 q^{13} - 6 q^{14} - 4 q^{15} - 14 q^{16} - 6 q^{17} + 8 q^{18} - 2 q^{19} + 8 q^{21} + 6 q^{22} - 6 q^{23} - 2 q^{24} - 8 q^{25} - 4 q^{26} + 16 q^{27} + 6 q^{29} + 16 q^{30} - 16 q^{31} - 24 q^{32} - 24 q^{33} + 10 q^{34} + 2 q^{35} + 6 q^{36} + 8 q^{37} - 6 q^{38} + 12 q^{39} - 18 q^{40} + 16 q^{41} + 38 q^{42} + 4 q^{43} + 36 q^{44} - 8 q^{45} - 24 q^{46} - 16 q^{48} - 16 q^{49} + 4 q^{50} - 4 q^{51} + 42 q^{52} + 24 q^{54} - 52 q^{56} - 28 q^{57} - 68 q^{58} + 14 q^{59} - 6 q^{60} + 4 q^{61} - 24 q^{62} - 2 q^{63} + 80 q^{64} + 40 q^{65} + 2 q^{66} + 14 q^{67} + 76 q^{68} - 28 q^{69} + 8 q^{70} + 12 q^{71} - 28 q^{72} + 34 q^{73} - 18 q^{74} + 4 q^{75} + 46 q^{76} - 28 q^{77} - 12 q^{78} + 2 q^{79} + 20 q^{81} - 52 q^{82} + 20 q^{83} - 128 q^{84} + 8 q^{85} + 24 q^{86} + 4 q^{87} - 32 q^{88} + 18 q^{89} + 24 q^{90} + 12 q^{91} - 40 q^{92} - 12 q^{93} - 20 q^{94} - 12 q^{95} + 76 q^{96} - 16 q^{97} - 32 q^{98} - 28 q^{99} + O(q^{100}) \)

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.e.a 95.e 19.c $2$ $0.759$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(1\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
95.2.e.b 95.e 19.c $6$ $0.759$ 6.0.3518667.1 None \(-1\) \(-1\) \(3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{3}-\beta _{5})q^{3}+(-3+\cdots)q^{4}+\cdots\)
95.2.e.c 95.e 19.c $8$ $0.759$ 8.0.4601315889.1 None \(-1\) \(-3\) \(-4\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{7}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)