Properties

Label 3013.2.a
Level 3013
Weight 2
Character orbit a
Rep. character \(\chi_{3013}(1,\cdot)\)
Character field \(\Q\)
Dimension 237
Newforms 4
Sturm bound 528
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3013 = 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3013.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(528\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3013))\).

Total New Old
Modular forms 266 237 29
Cusp forms 263 237 26
Eisenstein series 3 0 3

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

\(23\)\(131\)FrickeDim.
\(+\)\(+\)\(+\)\(60\)
\(+\)\(-\)\(-\)\(58\)
\(-\)\(+\)\(-\)\(68\)
\(-\)\(-\)\(+\)\(51\)
Plus space\(+\)\(111\)
Minus space\(-\)\(126\)

Trace form

\( 237q + q^{2} + 237q^{4} - 2q^{5} + 12q^{6} - 4q^{7} + 9q^{8} + 233q^{9} + O(q^{10}) \) \( 237q + q^{2} + 237q^{4} - 2q^{5} + 12q^{6} - 4q^{7} + 9q^{8} + 233q^{9} - 10q^{10} + 4q^{11} - 26q^{13} + 4q^{15} + 217q^{16} - 18q^{17} + 29q^{18} + 6q^{20} - 12q^{21} + 12q^{22} + q^{23} + 60q^{24} + 231q^{25} + 14q^{26} + 12q^{27} + 16q^{28} - 2q^{29} + 56q^{30} - 8q^{31} + 49q^{32} + 30q^{33} + 18q^{34} + 10q^{35} + 261q^{36} - 30q^{37} + 24q^{38} - 34q^{39} - 22q^{40} + 2q^{41} + 20q^{42} - 28q^{43} - 36q^{44} - 36q^{45} - q^{46} + 20q^{47} + 20q^{48} + 225q^{49} - 5q^{50} + 4q^{51} - 30q^{52} - 16q^{53} + 20q^{54} + 4q^{55} - 8q^{56} - 24q^{57} - 18q^{58} - 16q^{59} - 76q^{60} - 50q^{61} - 48q^{62} - 30q^{63} + 209q^{64} - 20q^{65} - 52q^{66} + 28q^{67} - 54q^{68} + 4q^{69} + 36q^{70} - 44q^{71} + 61q^{72} - 34q^{73} - 22q^{74} - 14q^{75} + 28q^{76} + 4q^{77} - 60q^{78} - 8q^{79} - 98q^{80} + 245q^{81} + 26q^{82} + 36q^{83} - 104q^{84} - 4q^{85} + 84q^{86} + 32q^{87} - 72q^{88} + 28q^{89} - 42q^{90} - 48q^{91} + 7q^{92} + 8q^{93} + 20q^{94} - 12q^{95} + 156q^{96} - 14q^{97} - 103q^{98} + 60q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3013))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 23 131
3013.2.a.a \(51\) \(24.059\) None \(-14\) \(-20\) \(-7\) \(-5\) \(-\) \(-\)
3013.2.a.b \(58\) \(24.059\) None \(13\) \(16\) \(9\) \(7\) \(+\) \(-\)
3013.2.a.c \(60\) \(24.059\) None \(-12\) \(-18\) \(-13\) \(-13\) \(+\) \(+\)
3013.2.a.d \(68\) \(24.059\) None \(14\) \(22\) \(9\) \(7\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3013))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3013)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(131))\)\(^{\oplus 2}\)