Properties

Label 51.2.h
Level 51
Weight 2
Character orbit h
Rep. character \(\chi_{51}(19,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 8
Newforms 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 51 = 3 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 51.h (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Newforms: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(51, [\chi])\).

Total New Old
Modular forms 32 8 24
Cusp forms 16 8 8
Eisenstein series 16 0 16

Trace form

\( 8q - 8q^{5} - 8q^{6} + O(q^{10}) \) \( 8q - 8q^{5} - 8q^{6} + 8q^{11} - 16q^{14} + 16q^{16} - 8q^{17} - 8q^{19} + 16q^{20} - 8q^{22} + 8q^{23} + 8q^{24} - 16q^{25} + 16q^{26} - 8q^{28} + 8q^{31} + 8q^{33} - 8q^{34} + 32q^{35} + 8q^{36} - 8q^{37} + 16q^{39} - 8q^{40} - 24q^{41} + 8q^{42} - 8q^{43} - 8q^{45} - 8q^{49} - 32q^{50} - 16q^{52} - 32q^{53} - 8q^{54} - 16q^{56} - 16q^{57} + 24q^{58} + 16q^{59} - 8q^{60} + 16q^{61} + 16q^{62} + 24q^{65} - 16q^{66} - 16q^{67} - 24q^{69} + 40q^{70} - 16q^{71} + 48q^{73} + 64q^{74} + 16q^{75} + 24q^{76} + 8q^{78} - 16q^{80} - 8q^{82} + 32q^{83} + 40q^{85} - 32q^{86} + 24q^{87} - 8q^{88} - 16q^{91} - 32q^{92} - 32q^{93} - 40q^{95} - 16q^{96} + 8q^{97} + 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(51, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
51.2.h.a \(8\) \(0.407\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(-8\) \(0\) \(q+(\zeta_{16}+\zeta_{16}^{3})q^{2}+\zeta_{16}^{7}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(51, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(51, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 2}\)