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Properties

Label 195.2.k
Level $195$
Weight $2$
Character orbit 195.k
Rep. character $\chi_{195}(112,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $28$
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.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(i)\)
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 28 36
Cusp forms 48 28 20
Eisenstein series 16 0 16

Trace form

\( 28 q - 28 q^{4} + 8 q^{5} + O(q^{10}) \) \( 28 q - 28 q^{4} + 8 q^{5} - 8 q^{11} + 8 q^{12} - 12 q^{13} + 4 q^{15} + 28 q^{16} - 28 q^{17} - 4 q^{18} + 8 q^{21} - 32 q^{22} + 8 q^{23} - 4 q^{25} - 16 q^{31} + 28 q^{34} + 32 q^{37} + 8 q^{39} - 48 q^{40} + 4 q^{41} + 40 q^{44} - 4 q^{45} - 16 q^{46} - 24 q^{47} - 16 q^{48} - 28 q^{49} - 32 q^{50} + 52 q^{52} + 20 q^{53} - 8 q^{55} - 8 q^{58} + 32 q^{59} - 12 q^{60} + 8 q^{61} + 72 q^{62} - 28 q^{64} - 8 q^{65} + 16 q^{66} + 60 q^{68} + 8 q^{69} + 64 q^{70} + 40 q^{71} + 12 q^{72} - 16 q^{75} - 40 q^{76} - 48 q^{77} + 8 q^{78} - 32 q^{80} - 28 q^{81} + 4 q^{82} - 104 q^{83} - 32 q^{84} - 4 q^{85} + 16 q^{86} - 24 q^{87} + 72 q^{88} - 36 q^{89} - 12 q^{90} - 56 q^{91} - 32 q^{92} + 56 q^{95} + 8 q^{99} + O(q^{100}) \)

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.k.a 195.k 65.f $28$ $1.557$ None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

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