Properties

Label 195.2.a
Level $195$
Weight $2$
Character orbit 195.a
Rep. character $\chi_{195}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $5$
Sturm bound $56$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 195 = 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 195.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(56\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(195))\).

Total New Old
Modular forms 32 7 25
Cusp forms 25 7 18
Eisenstein series 7 0 7

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

\(3\)\(5\)\(13\)FrickeDim.
\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(2\)
Plus space\(+\)\(0\)
Minus space\(-\)\(7\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(195))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 13
195.2.a.a \(1\) \(1.557\) \(\Q\) None \(-1\) \(1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+3q^{8}+\cdots\)
195.2.a.b \(1\) \(1.557\) \(\Q\) None \(2\) \(-1\) \(1\) \(3\) \(+\) \(-\) \(+\) \(q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+3q^{7}+\cdots\)
195.2.a.c \(1\) \(1.557\) \(\Q\) None \(2\) \(1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-q^{7}+\cdots\)
195.2.a.d \(1\) \(1.557\) \(\Q\) None \(2\) \(1\) \(1\) \(-3\) \(-\) \(-\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-3q^{7}+\cdots\)
195.2.a.e \(3\) \(1.557\) 3.3.316.1 None \(0\) \(-3\) \(-3\) \(1\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(3+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(195))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(195)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 2}\)