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Properties

Label 147.2.k
Level $147$
Weight $2$
Character orbit 147.k
Rep. character $\chi_{147}(20,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $96$
Newform subspaces $1$
Sturm bound $37$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 147.k (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 1 \)
Sturm bound: \(37\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(147, [\chi])\).

Total New Old
Modular forms 120 120 0
Cusp forms 96 96 0
Eisenstein series 24 24 0

Trace form

\( 96 q - 7 q^{3} + 2 q^{4} + 7 q^{6} - 14 q^{7} + 5 q^{9} + O(q^{10}) \) \( 96 q - 7 q^{3} + 2 q^{4} + 7 q^{6} - 14 q^{7} + 5 q^{9} - 14 q^{10} - 42 q^{12} - 14 q^{13} - 5 q^{15} - 22 q^{16} - 18 q^{18} - 7 q^{21} + 4 q^{22} - 7 q^{24} - 26 q^{25} - 28 q^{27} + 28 q^{28} - 20 q^{30} - 7 q^{33} - 70 q^{34} - 37 q^{36} + 38 q^{37} - 9 q^{39} - 28 q^{40} + 7 q^{42} - 18 q^{43} + 14 q^{45} + 62 q^{46} + 14 q^{49} - q^{51} + 112 q^{52} - 7 q^{54} - 56 q^{55} + q^{57} - 84 q^{58} + 111 q^{60} + 84 q^{61} - 7 q^{63} - 2 q^{64} + 21 q^{66} - 16 q^{67} - 91 q^{69} - 70 q^{70} - 27 q^{72} - 14 q^{73} + 119 q^{75} + 210 q^{76} - 87 q^{78} - 32 q^{79} - 71 q^{81} - 84 q^{82} + 154 q^{84} + 46 q^{85} + 49 q^{87} - 22 q^{88} + 203 q^{90} - 42 q^{91} + 53 q^{93} - 42 q^{94} - 28 q^{96} + 100 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(147, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
147.2.k.a 147.k 147.k $96$ $1.174$ None \(0\) \(-7\) \(0\) \(-14\) $\mathrm{SU}(2)[C_{14}]$