Properties

Label 8035.2.a
Level 8035
Weight 2
Character orbit a
Rep. character \(\chi_{8035}(1,\cdot)\)
Character field \(\Q\)
Dimension 535
Newforms 5
Sturm bound 1608
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8035.a (trivial)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(1608\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8035))\).

Total New Old
Modular forms 806 535 271
Cusp forms 803 535 268
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.

\(5\)\(1607\)FrickeDim.
\(+\)\(+\)\(+\)\(140\)
\(+\)\(-\)\(-\)\(127\)
\(-\)\(+\)\(-\)\(154\)
\(-\)\(-\)\(+\)\(114\)
Plus space\(+\)\(254\)
Minus space\(-\)\(281\)

Trace form

\( 535q + q^{2} - 4q^{3} + 537q^{4} + q^{5} - 4q^{6} - 4q^{7} - 3q^{8} + 527q^{9} + O(q^{10}) \) \( 535q + q^{2} - 4q^{3} + 537q^{4} + q^{5} - 4q^{6} - 4q^{7} - 3q^{8} + 527q^{9} + 3q^{10} + 4q^{11} - 8q^{12} - 6q^{13} + 16q^{14} + 545q^{16} - 6q^{17} + q^{18} - 8q^{19} - q^{20} - 4q^{21} + 24q^{22} + 8q^{23} + 8q^{24} + 535q^{25} - 30q^{26} - 28q^{27} - 4q^{28} + 10q^{29} - 4q^{30} - 15q^{32} - 28q^{33} + 14q^{34} + 493q^{36} - 6q^{37} - 32q^{38} - 16q^{39} + 15q^{40} + 6q^{41} - 4q^{42} - 8q^{43} - 32q^{44} + 13q^{45} + 44q^{46} + 32q^{47} - 52q^{48} + 539q^{49} + q^{50} + 12q^{51} - 14q^{52} + 2q^{53} - 44q^{54} - 4q^{55} - 20q^{56} - 72q^{57} + 26q^{58} - 12q^{59} - 16q^{60} + 10q^{61} - 80q^{62} - 8q^{63} + 557q^{64} - 2q^{65} - 64q^{66} + 8q^{67} - 66q^{68} - 40q^{69} + 12q^{70} - 48q^{71} - 39q^{72} - 58q^{73} + 2q^{74} - 4q^{75} - 20q^{76} - 28q^{77} - 64q^{78} + 8q^{79} - q^{80} + 479q^{81} - 78q^{82} + 12q^{83} + 6q^{85} - 24q^{86} + 28q^{87} + 36q^{88} + 10q^{89} + 23q^{90} - 24q^{91} + 28q^{92} - 64q^{93} + 8q^{94} - 12q^{95} - 4q^{96} - 26q^{97} - 55q^{98} + 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8035))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 1607
8035.2.a.a \(1\) \(64.160\) \(\Q\) None \(1\) \(1\) \(1\) \(4\) \(-\) \(+\) \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+4q^{7}+\cdots\)
8035.2.a.b \(114\) \(64.160\) None \(-17\) \(-10\) \(114\) \(-11\) \(-\) \(-\)
8035.2.a.c \(127\) \(64.160\) None \(19\) \(10\) \(-127\) \(13\) \(+\) \(-\)
8035.2.a.d \(140\) \(64.160\) None \(-20\) \(-12\) \(-140\) \(-15\) \(+\) \(+\)
8035.2.a.e \(153\) \(64.160\) None \(18\) \(7\) \(153\) \(5\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8035))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8035)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(1607))\)\(^{\oplus 2}\)