Properties

Label 195.2.v
Level $195$
Weight $2$
Character orbit 195.v
Rep. character $\chi_{195}(4,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
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.v (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 32 32
Cusp forms 48 32 16
Eisenstein series 16 0 16

Trace form

\( 32q - 20q^{4} + 16q^{9} + O(q^{10}) \) \( 32q - 20q^{4} + 16q^{9} + 2q^{10} - 12q^{11} + 8q^{14} - 6q^{15} - 28q^{16} - 30q^{20} - 4q^{25} + 52q^{26} - 24q^{29} + 4q^{30} - 2q^{35} + 20q^{36} + 4q^{40} - 36q^{41} + 12q^{45} - 48q^{46} - 28q^{49} + 54q^{50} - 40q^{51} + 24q^{55} - 56q^{56} + 84q^{59} - 32q^{61} + 136q^{64} + 20q^{65} + 8q^{66} - 24q^{69} + 12q^{71} + 40q^{74} - 16q^{75} + 48q^{76} - 104q^{79} + 66q^{80} - 16q^{81} - 48q^{84} - 54q^{85} - 48q^{89} + 4q^{90} + 12q^{91} - 8q^{94} + 12q^{95} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
195.2.v.a \(32\) \(1.557\) None \(0\) \(0\) \(0\) \(0\)

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

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