Properties

Label 51.2.i
Level 51
Weight 2
Character orbit i
Rep. character \(\chi_{51}(5,\cdot)\)
Character field \(\Q(\zeta_{16})\)
Dimension 32
Newform subspaces 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.i (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 51 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 1 \)
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 64 64 0
Cusp forms 32 32 0
Eisenstein series 32 32 0

Trace form

\( 32q - 8q^{3} - 16q^{4} - 8q^{6} - 16q^{7} - 8q^{9} + O(q^{10}) \) \( 32q - 8q^{3} - 16q^{4} - 8q^{6} - 16q^{7} - 8q^{9} - 16q^{10} + 16q^{12} - 16q^{13} + 16q^{15} + 16q^{18} - 16q^{19} + 16q^{21} - 16q^{22} + 16q^{24} + 16q^{25} - 8q^{27} + 32q^{28} - 8q^{30} + 16q^{31} + 96q^{34} + 8q^{36} + 16q^{37} - 24q^{39} + 16q^{40} - 56q^{42} + 16q^{43} - 40q^{45} - 32q^{46} - 64q^{48} - 48q^{49} - 40q^{51} - 96q^{52} - 24q^{54} - 48q^{55} + 8q^{57} - 48q^{58} + 32q^{60} - 32q^{61} + 64q^{63} + 16q^{64} + 72q^{66} + 80q^{69} + 48q^{70} + 64q^{72} + 48q^{73} + 88q^{75} + 48q^{76} + 96q^{78} + 16q^{79} + 48q^{81} + 112q^{82} - 56q^{87} + 16q^{88} - 88q^{90} + 16q^{91} - 72q^{93} - 48q^{94} - 112q^{96} - 16q^{97} - 64q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(51, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
51.2.i.a \(32\) \(0.407\) None \(0\) \(-8\) \(0\) \(-16\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database