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Properties

Label 93.2.k
Level $93$
Weight $2$
Character orbit 93.k
Rep. character $\chi_{93}(23,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $32$
Newform subspaces $1$
Sturm bound $21$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 93 = 3 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 93.k (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 93 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(21\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(93, [\chi])\).

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

Trace form

\( 32 q - 5 q^{3} - 6 q^{4} + 8 q^{7} - q^{9} + O(q^{10}) \) \( 32 q - 5 q^{3} - 6 q^{4} + 8 q^{7} - q^{9} + 6 q^{10} - 30 q^{12} - 10 q^{13} + 5 q^{15} - 18 q^{16} - 21 q^{18} - 30 q^{19} - 5 q^{21} + 15 q^{24} - 8 q^{25} - 20 q^{27} + 56 q^{28} - 30 q^{31} + 4 q^{33} + 10 q^{34} + 14 q^{36} - 17 q^{39} - 2 q^{40} - 30 q^{42} + 50 q^{43} + 42 q^{45} + 40 q^{46} + 30 q^{48} + 8 q^{49} + 17 q^{51} - 30 q^{52} + 50 q^{54} + 20 q^{55} - 80 q^{58} + 95 q^{60} + 96 q^{63} - 64 q^{64} + 48 q^{66} - 44 q^{67} - 71 q^{69} + 44 q^{70} - 37 q^{72} + 5 q^{75} - 58 q^{76} - 25 q^{78} - 60 q^{79} + 51 q^{81} + 2 q^{82} - 25 q^{84} + 40 q^{85} - 54 q^{87} - 102 q^{90} - 70 q^{91} - 8 q^{93} - 128 q^{94} + 50 q^{96} - 66 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(93, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
93.2.k.a 93.k 93.k $32$ $0.743$ None \(0\) \(-5\) \(0\) \(8\) $\mathrm{SU}(2)[C_{10}]$