Properties

Label 195.2.ba
Level $195$
Weight $2$
Character orbit 195.ba
Rep. character $\chi_{195}(94,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
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.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
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 64 24 40
Cusp forms 48 24 24
Eisenstein series 16 0 16

Trace form

\( 24 q + 8 q^{4} + 4 q^{5} + 12 q^{9} + O(q^{10}) \) \( 24 q + 8 q^{4} + 4 q^{5} + 12 q^{9} - 4 q^{10} + 4 q^{11} + 24 q^{14} - 2 q^{15} + 16 q^{16} - 16 q^{19} - 16 q^{20} - 8 q^{21} - 16 q^{25} - 48 q^{26} - 12 q^{29} - 4 q^{30} + 8 q^{31} - 32 q^{34} + 10 q^{35} - 8 q^{36} + 8 q^{39} - 48 q^{40} - 40 q^{41} + 40 q^{44} + 2 q^{45} - 24 q^{46} - 16 q^{49} + 20 q^{50} - 24 q^{51} + 20 q^{55} - 24 q^{56} + 12 q^{59} + 48 q^{60} + 20 q^{61} + 48 q^{64} + 14 q^{65} - 56 q^{66} - 8 q^{69} - 56 q^{70} + 4 q^{71} - 12 q^{74} + 16 q^{75} + 8 q^{76} + 136 q^{79} - 4 q^{80} - 12 q^{81} - 16 q^{84} - 4 q^{85} + 48 q^{86} - 64 q^{89} - 8 q^{90} + 60 q^{91} - 48 q^{94} - 28 q^{95} + 40 q^{96} + 8 q^{99} + O(q^{100}) \)

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.ba.a 195.ba 65.n $24$ $1.557$ None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(195, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)