Properties

Label 195.2.bd
Level $195$
Weight $2$
Character orbit 195.bd
Rep. character $\chi_{195}(67,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $56$
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.bd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
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 56 72
Cusp forms 96 56 40
Eisenstein series 32 0 32

Trace form

\( 56 q + 4 q^{2} - 28 q^{4} + 4 q^{5} - 24 q^{8} + O(q^{10}) \) \( 56 q + 4 q^{2} - 28 q^{4} + 4 q^{5} - 24 q^{8} + 8 q^{11} - 16 q^{12} - 12 q^{13} + 4 q^{15} - 28 q^{16} + 8 q^{17} - 24 q^{19} - 12 q^{20} - 8 q^{21} - 28 q^{22} + 8 q^{23} + 20 q^{25} - 8 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 24 q^{37} + 8 q^{39} + 24 q^{40} - 4 q^{41} + 60 q^{42} + 12 q^{43} + 40 q^{44} - 16 q^{45} - 8 q^{46} + 16 q^{48} + 44 q^{49} - 52 q^{50} - 24 q^{52} + 4 q^{53} - 40 q^{55} + 72 q^{56} + 120 q^{58} - 64 q^{59} + 16 q^{61} + 36 q^{62} + 56 q^{64} - 4 q^{65} - 16 q^{66} + 64 q^{67} + 48 q^{68} + 8 q^{69} + 16 q^{70} - 16 q^{71} - 80 q^{73} + 36 q^{74} - 16 q^{75} + 112 q^{76} - 48 q^{77} - 40 q^{78} - 36 q^{80} + 28 q^{81} - 32 q^{82} - 32 q^{84} - 56 q^{85} - 64 q^{86} - 60 q^{87} - 120 q^{88} - 12 q^{89} + 12 q^{90} - 40 q^{91} - 64 q^{92} - 24 q^{94} - 40 q^{95} - 12 q^{97} + 108 q^{98} + 8 q^{99} + O(q^{100}) \)

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.bd.a 195.bd 65.o $56$ $1.557$ None \(4\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{12}]$

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

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