Properties

Label 93.2.a
Level $93$
Weight $2$
Character orbit 93.a
Rep. character $\chi_{93}(1,\cdot)$
Character field $\Q$
Dimension $5$
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.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(21\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(93))\).

Total New Old
Modular forms 12 5 7
Cusp forms 9 5 4
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(31\)FrickeDim.
\(+\)\(+\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(3\)
Plus space\(+\)\(2\)
Minus space\(-\)\(3\)

Trace form

\( 5 q - 3 q^{2} + q^{3} + 5 q^{4} - 6 q^{5} + 3 q^{6} - 9 q^{8} + 5 q^{9} + O(q^{10}) \) \( 5 q - 3 q^{2} + q^{3} + 5 q^{4} - 6 q^{5} + 3 q^{6} - 9 q^{8} + 5 q^{9} - 4 q^{10} - 8 q^{11} - q^{12} + 2 q^{13} + 6 q^{14} + 2 q^{15} + 9 q^{16} - 6 q^{17} - 3 q^{18} - 4 q^{19} + 8 q^{21} + 8 q^{22} - 4 q^{23} + 3 q^{24} + 7 q^{25} + 2 q^{26} + q^{27} - 26 q^{28} - 6 q^{29} - 6 q^{30} - 5 q^{31} - 11 q^{32} + 4 q^{33} + 6 q^{34} + 8 q^{35} + 5 q^{36} + 2 q^{37} + 34 q^{38} + 6 q^{39} - 6 q^{40} - 10 q^{41} - 16 q^{42} + 8 q^{43} - 4 q^{44} - 6 q^{45} - 24 q^{46} + 16 q^{47} - 17 q^{48} + q^{49} + 29 q^{50} + 2 q^{51} + 6 q^{52} - 10 q^{53} + 3 q^{54} - 12 q^{55} + 28 q^{56} + 12 q^{57} - 2 q^{58} + 20 q^{59} - 18 q^{60} + 14 q^{61} + 3 q^{62} - 17 q^{64} - 24 q^{65} - 20 q^{66} - 12 q^{67} + 38 q^{68} - 8 q^{69} + 14 q^{70} + 8 q^{71} - 9 q^{72} - 10 q^{73} - 2 q^{74} - 9 q^{75} - 14 q^{76} + 4 q^{77} - 14 q^{78} + 16 q^{79} + 12 q^{80} + 5 q^{81} - 12 q^{82} - 4 q^{83} + 16 q^{84} + 4 q^{85} - 32 q^{86} - 10 q^{87} + 40 q^{88} - 22 q^{89} - 4 q^{90} + 4 q^{91} + 20 q^{92} - q^{93} + 16 q^{94} + 16 q^{95} + 19 q^{96} + 22 q^{97} - 25 q^{98} - 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(93))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 31
93.2.a.a 93.a 1.a $2$ $0.743$ \(\Q(\sqrt{5}) \) None \(-3\) \(-2\) \(-4\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(-3+\cdots)q^{5}+\cdots\)
93.2.a.b 93.a 1.a $3$ $0.743$ 3.3.229.1 None \(0\) \(3\) \(-2\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(93))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(93)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 2}\)