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

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

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 \(11\) \(53\) \(5\) \(46\) \(-\)