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

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

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

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