Properties

Label 95.2.a
Level $95$
Weight $2$
Character orbit 95.a
Rep. character $\chi_{95}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $2$
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.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(20\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(95))\).

Total New Old
Modular forms 12 7 5
Cusp forms 9 7 2
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.

\(5\)\(19\)FrickeDim.
\(+\)\(-\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(3\)
Plus space\(+\)\(0\)
Minus space\(-\)\(7\)

Trace form

\( 7q - q^{2} + 4q^{3} + 9q^{4} - q^{5} - 4q^{6} + 4q^{7} - 9q^{8} + 11q^{9} + O(q^{10}) \) \( 7q - q^{2} + 4q^{3} + 9q^{4} - q^{5} - 4q^{6} + 4q^{7} - 9q^{8} + 11q^{9} + 3q^{10} - 4q^{11} - 4q^{12} + 10q^{13} - 12q^{14} + q^{16} + 6q^{17} - 29q^{18} + q^{19} - 7q^{20} - 16q^{21} - 12q^{22} - 12q^{23} - 28q^{24} + 7q^{25} - 2q^{26} + 4q^{27} + 4q^{28} - 6q^{29} - 4q^{30} + 8q^{31} - 9q^{32} + 12q^{33} + 14q^{34} - 4q^{35} + 29q^{36} + 14q^{37} - 3q^{38} - 8q^{39} + 15q^{40} + 14q^{41} + 16q^{42} + 12q^{44} - 5q^{45} + 12q^{46} - 12q^{47} + 48q^{48} + 31q^{49} - q^{50} - 32q^{51} + 22q^{52} + 6q^{53} - 12q^{55} + 4q^{56} + 2q^{58} - 20q^{59} - 16q^{60} + 18q^{61} + 48q^{62} - 12q^{63} - 15q^{64} + 6q^{65} - 8q^{66} - 16q^{67} + 2q^{68} + 16q^{69} + 4q^{70} - 24q^{71} - 65q^{72} + 30q^{73} + 30q^{74} + 4q^{75} + 7q^{76} - 32q^{77} - 16q^{79} - 7q^{80} + 15q^{81} - 2q^{82} - 32q^{83} - 24q^{84} - 2q^{85} - 24q^{86} - 64q^{87} - 16q^{88} + 6q^{89} + 39q^{90} - 16q^{91} - 20q^{92} - 56q^{93} - 52q^{94} - 7q^{95} - 28q^{96} + 50q^{97} + 23q^{98} - 20q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(95))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 19
95.2.a.a \(3\) \(0.759\) 3.3.148.1 None \(1\) \(2\) \(3\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
95.2.a.b \(4\) \(0.759\) 4.4.11344.1 None \(-2\) \(2\) \(-4\) \(4\) \(+\) \(-\) \(q+\beta _{2}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(95))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(95)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 2}\)