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Properties

Label 93.2.e
Level $93$
Weight $2$
Character orbit 93.e
Rep. character $\chi_{93}(25,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $10$
Newform subspaces $2$
Sturm bound $21$
Trace bound $1$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 26 10 16
Cusp forms 18 10 8
Eisenstein series 8 0 8

Trace form

\( 10 q - q^{3} + 4 q^{4} + 12 q^{8} - 5 q^{9} + O(q^{10}) \) \( 10 q - q^{3} + 4 q^{4} + 12 q^{8} - 5 q^{9} - 8 q^{10} + 2 q^{11} - 2 q^{12} - 5 q^{13} - 18 q^{14} + 16 q^{15} - 24 q^{16} - 6 q^{17} + 7 q^{19} - 18 q^{20} - 8 q^{21} + 16 q^{22} + 16 q^{23} - 6 q^{24} - 19 q^{25} - 2 q^{26} + 2 q^{27} - 4 q^{28} + 8 q^{31} - 16 q^{32} - 4 q^{33} + 12 q^{34} + 28 q^{35} - 2 q^{36} + q^{37} + 14 q^{38} + 18 q^{39} + 4 q^{41} - 2 q^{42} - 5 q^{43} - 2 q^{44} - 4 q^{47} - 4 q^{48} - 13 q^{49} + 10 q^{50} + 10 q^{51} + 6 q^{52} + 10 q^{53} - 12 q^{55} + 8 q^{56} + 3 q^{57} + 32 q^{58} + 16 q^{59} + 36 q^{60} + 4 q^{61} + 12 q^{62} + 8 q^{64} - 6 q^{65} - 16 q^{66} - 12 q^{67} + 4 q^{68} - 16 q^{69} + 40 q^{70} - 32 q^{71} - 6 q^{72} - 5 q^{73} - 34 q^{74} - 15 q^{75} + 14 q^{76} - 76 q^{77} - 28 q^{78} - 16 q^{79} + 12 q^{80} - 5 q^{81} + 12 q^{82} + 28 q^{83} - 4 q^{84} + 8 q^{85} + 38 q^{86} - 8 q^{87} - 4 q^{88} - 20 q^{89} - 8 q^{90} + 56 q^{91} - 8 q^{92} - 23 q^{93} - 88 q^{94} - 52 q^{95} + 8 q^{96} - 46 q^{97} + 16 q^{98} + 2 q^{99} + O(q^{100}) \)

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.e.a 93.e 31.c $4$ $0.743$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{2}+(1+\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
93.2.e.b 93.e 31.c $6$ $0.743$ 6.0.591408.1 None \(0\) \(-3\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{2}-\beta _{4}q^{3}+(1-\beta _{2}+\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(93, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(93, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 2}\)