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Properties

Label 195.2.s
Level $195$
Weight $2$
Character orbit 195.s
Rep. character $\chi_{195}(38,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $48$
Newform subspaces $2$
Sturm bound $56$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 195 = 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 195.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 195 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(56\)
Trace bound: \(1\)
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 64 0
Cusp forms 48 48 0
Eisenstein series 16 16 0

Trace form

\( 48 q - 4 q^{3} + O(q^{10}) \) \( 48 q - 4 q^{3} - 16 q^{10} - 40 q^{16} - 32 q^{22} - 8 q^{25} - 16 q^{27} - 36 q^{30} + 88 q^{36} + 104 q^{40} + 12 q^{42} - 32 q^{43} - 68 q^{48} + 16 q^{51} + 32 q^{52} - 80 q^{55} + 8 q^{61} - 72 q^{66} + 44 q^{75} + 84 q^{78} - 32 q^{81} - 88 q^{82} + 20 q^{87} + 96 q^{88} + 44 q^{90} - 40 q^{91} + O(q^{100}) \)

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.s.a 195.s 195.s $16$ $1.557$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) \(\Q(\sqrt{-39}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(2\beta _{2}+\beta _{12})q^{4}+\cdots\)
195.2.s.b 195.s 195.s $32$ $1.557$ None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$