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Properties

Label 195.2.i
Level $195$
Weight $2$
Character orbit 195.i
Rep. character $\chi_{195}(16,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $20$
Newform subspaces $5$
Sturm bound $56$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 195 = 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 195.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 5 \)
Sturm bound: \(56\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(195, [\chi])\).

Total New Old
Modular forms 64 20 44
Cusp forms 48 20 28
Eisenstein series 16 0 16

Trace form

\( 20 q + 2 q^{3} - 12 q^{4} - 2 q^{7} - 10 q^{9} + O(q^{10}) \) \( 20 q + 2 q^{3} - 12 q^{4} - 2 q^{7} - 10 q^{9} + 4 q^{10} - 8 q^{11} - 8 q^{12} + 10 q^{13} + 8 q^{14} - 24 q^{16} + 4 q^{17} - 8 q^{20} + 12 q^{21} + 4 q^{22} - 12 q^{23} + 24 q^{24} + 20 q^{25} - 32 q^{26} - 4 q^{27} - 36 q^{28} + 8 q^{29} + 4 q^{30} - 12 q^{31} + 20 q^{32} + 16 q^{34} - 4 q^{35} - 12 q^{36} + 8 q^{37} + 80 q^{38} + 4 q^{39} - 24 q^{40} + 32 q^{41} - 4 q^{42} + 2 q^{43} - 8 q^{44} + 8 q^{46} - 48 q^{47} - 8 q^{48} - 28 q^{49} + 8 q^{51} + 28 q^{52} - 64 q^{53} + 16 q^{55} - 8 q^{56} - 48 q^{57} - 8 q^{58} - 16 q^{59} + 18 q^{61} + 12 q^{62} - 2 q^{63} - 16 q^{64} + 4 q^{65} + 40 q^{66} + 6 q^{67} + 72 q^{68} + 4 q^{69} + 16 q^{70} + 8 q^{71} + 52 q^{73} + 44 q^{74} + 2 q^{75} - 8 q^{76} - 40 q^{77} + 16 q^{78} + 12 q^{79} - 32 q^{80} - 10 q^{81} + 8 q^{82} - 8 q^{83} - 12 q^{84} - 48 q^{86} + 32 q^{87} + 16 q^{88} - 48 q^{89} - 8 q^{90} - 10 q^{91} + 104 q^{92} - 6 q^{93} - 56 q^{94} - 8 q^{95} - 56 q^{96} - 26 q^{97} - 72 q^{98} + 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(195, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
195.2.i.a 195.i 13.c $2$ $1.557$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-1\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
195.2.i.b 195.i 13.c $2$ $1.557$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{4}-q^{5}+\zeta_{6}q^{7}+\cdots\)
195.2.i.c 195.i 13.c $4$ $1.557$ \(\Q(\zeta_{12})\) None \(2\) \(-2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}-\zeta_{12}q^{3}+(-2+\cdots)q^{4}+\cdots\)
195.2.i.d 195.i 13.c $6$ $1.557$ 6.0.1714608.1 None \(0\) \(3\) \(6\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{3}+\beta _{5})q^{2}+(1+\beta _{4})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
195.2.i.e 195.i 13.c $6$ $1.557$ 6.0.591408.1 None \(0\) \(3\) \(-6\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{5}q^{2}+(1-\beta _{4})q^{3}+(\beta _{1}-\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(195, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(195, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)