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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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(195))\) 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 5 13
195.2.a.a 195.a 1.a $1$ $1.557$ \(\Q\) None \(-1\) \(1\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+3q^{8}+\cdots\)
195.2.a.b 195.a 1.a $1$ $1.557$ \(\Q\) None \(2\) \(-1\) \(1\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+3q^{7}+\cdots\)
195.2.a.c 195.a 1.a $1$ $1.557$ \(\Q\) None \(2\) \(1\) \(-1\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-q^{7}+\cdots\)
195.2.a.d 195.a 1.a $1$ $1.557$ \(\Q\) None \(2\) \(1\) \(1\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-3q^{7}+\cdots\)
195.2.a.e 195.a 1.a $3$ $1.557$ 3.3.316.1 None \(0\) \(-3\) \(-3\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(3+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)

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

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