Properties

Label 1511.2.a
Level 1511
Weight 2
Character orbit a
Rep. character \(\chi_{1511}(1,\cdot)\)
Character field \(\Q\)
Dimension 126
Newform subspaces 2
Sturm bound 252
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 1511 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1511.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(252\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1511))\).

Total New Old
Modular forms 127 127 0
Cusp forms 126 126 0
Eisenstein series 1 1 0

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(1511\)Dim.
\(+\)\(39\)
\(-\)\(87\)

Trace form

\( 126q + q^{2} + 129q^{4} + 2q^{5} + 6q^{7} + 3q^{8} + 132q^{9} + O(q^{10}) \) \( 126q + q^{2} + 129q^{4} + 2q^{5} + 6q^{7} + 3q^{8} + 132q^{9} + 12q^{10} + 4q^{11} - 8q^{12} + 10q^{13} + 139q^{16} + 6q^{17} - 3q^{18} + 16q^{19} - 12q^{20} + 12q^{21} + 6q^{22} - 8q^{24} + 144q^{25} + 8q^{26} - 12q^{27} + 14q^{28} + 10q^{29} + 8q^{30} + 10q^{31} + 17q^{32} + 6q^{33} + 4q^{34} + 20q^{35} + 157q^{36} + 8q^{37} - 14q^{38} + 30q^{39} + 6q^{40} + 10q^{41} - 36q^{42} + 34q^{43} + 8q^{44} - 2q^{45} + 38q^{46} - 10q^{47} - 38q^{48} + 158q^{49} + 29q^{50} + 26q^{51} + 26q^{52} + 2q^{53} - 6q^{54} + 18q^{55} + 16q^{57} - 2q^{58} - 16q^{59} - 12q^{60} + 44q^{61} + 24q^{62} + 10q^{63} + 161q^{64} + 22q^{65} + 22q^{66} + 14q^{67} + 10q^{69} - 8q^{70} - 26q^{71} - 7q^{72} + 22q^{73} - 22q^{74} - 48q^{75} + 92q^{76} + 2q^{77} - 86q^{78} + 48q^{79} - 28q^{80} + 174q^{81} + 38q^{82} - 44q^{83} - 48q^{84} + 40q^{85} - 2q^{86} - 22q^{87} + 54q^{88} + 28q^{89} - 14q^{92} - 6q^{93} + 50q^{94} - 34q^{95} - 46q^{96} + 36q^{97} + q^{98} + 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1511))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 1511
1511.2.a.a \(39\) \(12.065\) None \(-5\) \(-4\) \(-8\) \(-15\) \(+\)
1511.2.a.b \(87\) \(12.065\) None \(6\) \(4\) \(10\) \(21\) \(-\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database