Properties

Label 4013.2.a
Level 4013
Weight 2
Character orbit a
Rep. character \(\chi_{4013}(1,\cdot)\)
Character field \(\Q\)
Dimension 334
Newforms 3
Sturm bound 669
Trace bound 1

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Defining parameters

Level: \( N \) = \( 4013 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4013.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(669\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4013))\).

Total New Old
Modular forms 335 335 0
Cusp forms 334 334 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.

\(4013\)Dim.
\(+\)\(157\)
\(-\)\(177\)

Trace form

\( 334q - 2q^{2} + 330q^{4} - 4q^{5} - 2q^{7} - 6q^{8} + 338q^{9} + O(q^{10}) \) \( 334q - 2q^{2} + 330q^{4} - 4q^{5} - 2q^{7} - 6q^{8} + 338q^{9} - 10q^{10} - 6q^{11} - 2q^{12} - 8q^{14} - 8q^{15} + 326q^{16} - 12q^{17} - 20q^{18} - 18q^{20} + 4q^{21} - 2q^{22} - 6q^{23} - 14q^{24} + 320q^{25} + 18q^{26} + 6q^{27} - 26q^{28} - 2q^{29} - 24q^{32} + 12q^{33} - 20q^{34} - 10q^{35} + 318q^{36} - 2q^{37} + 48q^{39} - 22q^{40} - 10q^{41} - 22q^{42} + 12q^{43} - 2q^{44} - 30q^{45} + 6q^{46} - 24q^{47} - 24q^{48} + 324q^{49} - 46q^{50} + 4q^{51} + 8q^{52} - 30q^{53} + 24q^{54} - 12q^{55} - 20q^{56} + 28q^{57} + 16q^{58} + 12q^{59} - 10q^{60} - 4q^{61} + 10q^{62} - 4q^{63} + 296q^{64} - 10q^{65} + 18q^{66} - 10q^{67} - 74q^{68} - 10q^{69} - 64q^{70} + 2q^{71} - 74q^{72} - 4q^{73} - 42q^{74} - 12q^{75} - 14q^{76} - 56q^{77} - 64q^{78} - 2q^{79} - 2q^{80} + 382q^{81} - 12q^{83} + 28q^{84} - 26q^{85} + 14q^{86} - 10q^{87} - 2q^{89} - 50q^{90} - 16q^{91} - 90q^{92} - 6q^{93} + 4q^{94} + 12q^{95} - 14q^{96} + 32q^{98} - 38q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4013))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 4013
4013.2.a.a \(1\) \(32.044\) \(\Q\) None \(2\) \(-2\) \(4\) \(1\) \(-\) \(q+2q^{2}-2q^{3}+2q^{4}+4q^{5}-4q^{6}+\cdots\)
4013.2.a.b \(157\) \(32.044\) None \(-15\) \(-51\) \(-13\) \(-49\) \(+\)
4013.2.a.c \(176\) \(32.044\) None \(11\) \(53\) \(5\) \(46\) \(-\)