Properties

Label 8047.2.a
Level 8047
Weight 2
Character orbit a
Rep. character \(\chi_{8047}(1,\cdot)\)
Character field \(\Q\)
Dimension 619
Newforms 5
Sturm bound 1446
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8047 = 13 \cdot 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8047.a (trivial)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(1446\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8047))\).

Total New Old
Modular forms 724 619 105
Cusp forms 721 619 102
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.

\(13\)\(619\)FrickeDim.
\(+\)\(+\)\(+\)\(151\)
\(+\)\(-\)\(-\)\(158\)
\(-\)\(+\)\(-\)\(168\)
\(-\)\(-\)\(+\)\(142\)
Plus space\(+\)\(293\)
Minus space\(-\)\(326\)

Trace form

\( 619q - q^{2} + 4q^{3} + 621q^{4} + 2q^{5} - 4q^{7} - 9q^{8} + 623q^{9} + O(q^{10}) \) \( 619q - q^{2} + 4q^{3} + 621q^{4} + 2q^{5} - 4q^{7} - 9q^{8} + 623q^{9} - 10q^{10} + 4q^{11} + 20q^{12} + q^{13} + 16q^{15} + 613q^{16} + 18q^{17} - 9q^{18} + 20q^{19} - 10q^{20} - 4q^{22} + 16q^{23} - 4q^{24} + 625q^{25} - 3q^{26} + 28q^{27} - 8q^{28} - 18q^{29} + 16q^{30} + 4q^{31} + 11q^{32} + 16q^{33} + 30q^{34} - 12q^{35} + 645q^{36} + 2q^{37} - 52q^{38} - 4q^{39} - 10q^{40} - 2q^{41} - 36q^{42} - 36q^{44} + 10q^{45} - 8q^{46} + 12q^{47} + 16q^{48} + 587q^{49} - 23q^{50} + 52q^{51} - q^{52} + 18q^{53} + 28q^{54} + 8q^{55} - 12q^{56} + 20q^{57} - 58q^{58} + 56q^{60} + 10q^{61} - 76q^{62} + 32q^{63} + 573q^{64} + 6q^{65} - 40q^{66} - 12q^{67} + 58q^{68} + 20q^{69} - 44q^{70} + 24q^{71} - 85q^{72} + 2q^{73} + 18q^{74} + 24q^{75} + 4q^{76} - 8q^{77} - 8q^{78} - 28q^{79} - 62q^{80} + 643q^{81} - 42q^{82} + 16q^{83} + 52q^{84} + 72q^{85} - 32q^{86} - 20q^{87} + 8q^{88} - 38q^{89} - 186q^{90} - 32q^{92} + 4q^{94} - 32q^{96} - 2q^{97} - 93q^{98} + 32q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8047))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 13 619
8047.2.a.a \(2\) \(64.256\) \(\Q(\sqrt{5}) \) None \(1\) \(-3\) \(2\) \(-3\) \(+\) \(-\) \(q+\beta q^{2}+(-1-\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
8047.2.a.b \(142\) \(64.256\) None \(-13\) \(-26\) \(-37\) \(-14\) \(-\) \(-\)
8047.2.a.c \(151\) \(64.256\) None \(-13\) \(-16\) \(-43\) \(-18\) \(+\) \(+\)
8047.2.a.d \(156\) \(64.256\) None \(13\) \(23\) \(39\) \(19\) \(+\) \(-\)
8047.2.a.e \(168\) \(64.256\) None \(11\) \(26\) \(41\) \(12\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8047))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8047)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(619))\)\(^{\oplus 2}\)