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Properties

Label 195.2.bg
Level $195$
Weight $2$
Character orbit 195.bg
Rep. character $\chi_{195}(11,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $72$
Newform subspaces $1$
Sturm bound $56$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 195 = 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 195.bg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(56\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 128 72 56
Cusp forms 96 72 24
Eisenstein series 32 0 32

Trace form

\( 72 q - 12 q^{6} + 12 q^{7} + O(q^{10}) \) \( 72 q - 12 q^{6} + 12 q^{7} - 4 q^{15} + 24 q^{16} - 40 q^{18} - 12 q^{19} - 36 q^{21} - 56 q^{24} + 24 q^{27} - 16 q^{28} - 48 q^{30} - 28 q^{31} - 8 q^{33} + 40 q^{34} + 12 q^{36} - 4 q^{37} + 32 q^{39} + 64 q^{42} - 84 q^{43} + 8 q^{45} + 64 q^{46} + 64 q^{48} - 84 q^{49} - 200 q^{52} + 32 q^{54} - 8 q^{55} + 36 q^{57} - 120 q^{58} - 16 q^{60} - 8 q^{61} - 8 q^{63} + 120 q^{66} + 64 q^{67} + 72 q^{69} + 24 q^{72} + 60 q^{73} - 8 q^{76} + 12 q^{78} - 16 q^{79} + 12 q^{81} + 120 q^{82} + 44 q^{84} - 48 q^{85} + 8 q^{87} - 144 q^{88} - 12 q^{91} - 36 q^{93} + 8 q^{94} + 4 q^{96} + 4 q^{97} - 40 q^{99} + O(q^{100}) \)

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.bg.a 195.bg 39.k $72$ $1.557$ None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{12}]$

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

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