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

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

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

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