Properties

Label 8013.2.a
Level 8013
Weight 2
Character orbit a
Rep. character \(\chi_{8013}(1,\cdot)\)
Character field \(\Q\)
Dimension 445
Newforms 4
Sturm bound 1781
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8013 = 3 \cdot 2671 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8013.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(1781\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8013))\).

Total New Old
Modular forms 892 445 447
Cusp forms 889 445 444
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.

\(3\)\(2671\)FrickeDim.
\(+\)\(+\)\(+\)\(116\)
\(+\)\(-\)\(-\)\(106\)
\(-\)\(+\)\(-\)\(129\)
\(-\)\(-\)\(+\)\(94\)
Plus space\(+\)\(210\)
Minus space\(-\)\(235\)

Trace form

\( 445q + q^{2} + q^{3} + 449q^{4} - 2q^{5} + 3q^{6} + 8q^{7} + 9q^{8} + 445q^{9} + O(q^{10}) \) \( 445q + q^{2} + q^{3} + 449q^{4} - 2q^{5} + 3q^{6} + 8q^{7} + 9q^{8} + 445q^{9} + 2q^{10} - q^{12} + 2q^{13} + 16q^{14} + 6q^{15} + 461q^{16} - 6q^{17} + q^{18} + 8q^{19} + 22q^{20} + 4q^{21} + 8q^{22} + 8q^{23} + 3q^{24} + 439q^{25} + 2q^{26} + q^{27} + 24q^{28} + 2q^{29} + 2q^{30} + 24q^{31} + 29q^{32} + 4q^{33} + 14q^{34} + 16q^{35} + 449q^{36} + 2q^{37} - 12q^{38} + 6q^{39} - 6q^{40} - 22q^{41} - 20q^{42} - 20q^{43} + 16q^{44} - 2q^{45} + 24q^{47} + 15q^{48} + 453q^{49} - 17q^{50} - 2q^{51} - 14q^{52} + 6q^{53} + 3q^{54} + 40q^{55} + 40q^{56} + 18q^{58} + 8q^{59} + 22q^{60} - 6q^{61} + 4q^{62} + 8q^{63} + 505q^{64} - 44q^{65} + 12q^{66} + 24q^{67} - 58q^{68} - 36q^{70} + 32q^{71} + 9q^{72} - 18q^{73} + 10q^{74} - 17q^{75} + 100q^{76} + 60q^{77} + 2q^{78} + 24q^{79} - 6q^{80} + 445q^{81} - 54q^{82} + 20q^{83} + 20q^{84} - 8q^{85} + 44q^{86} + 6q^{87} + 40q^{88} - 30q^{89} + 2q^{90} - 4q^{91} + 4q^{92} - 12q^{93} + 8q^{95} + 19q^{96} + 14q^{97} + 41q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8013))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 2671
8013.2.a.a \(94\) \(63.984\) None \(-13\) \(94\) \(-14\) \(-55\) \(-\) \(-\)
8013.2.a.b \(106\) \(63.984\) None \(15\) \(-106\) \(16\) \(35\) \(+\) \(-\)
8013.2.a.c \(116\) \(63.984\) None \(-16\) \(-116\) \(-20\) \(-33\) \(+\) \(+\)
8013.2.a.d \(129\) \(63.984\) None \(15\) \(129\) \(16\) \(61\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8013))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8013)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(2671))\)\(^{\oplus 2}\)