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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 31
93.2.a.a \(2\) \(0.743\) \(\Q(\sqrt{5}) \) None \(-3\) \(-2\) \(-4\) \(-4\) \(+\) \(+\) \(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(-3+\cdots)q^{5}+\cdots\)
93.2.a.b \(3\) \(0.743\) 3.3.229.1 None \(0\) \(3\) \(-2\) \(4\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)

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

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