Properties

Label 6035.2.a
Level 6035
Weight 2
Character orbit a
Rep. character \(\chi_{6035}(1,\cdot)\)
Character field \(\Q\)
Dimension 375
Newform subspaces 8
Sturm bound 1296
Trace bound 2

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Defining parameters

Level: \( N \) \(=\) \( 6035 = 5 \cdot 17 \cdot 71 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6035.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(1296\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6035))\).

Total New Old
Modular forms 652 375 277
Cusp forms 645 375 270
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(5\)\(17\)\(71\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(44\)
\(+\)\(+\)\(-\)\(-\)\(49\)
\(+\)\(-\)\(+\)\(-\)\(49\)
\(+\)\(-\)\(-\)\(+\)\(44\)
\(-\)\(+\)\(+\)\(-\)\(59\)
\(-\)\(+\)\(-\)\(+\)\(36\)
\(-\)\(-\)\(+\)\(+\)\(36\)
\(-\)\(-\)\(-\)\(-\)\(58\)
Plus space\(+\)\(160\)
Minus space\(-\)\(215\)

Trace form

\( 375q - 3q^{2} + 4q^{3} + 377q^{4} + 3q^{5} - 4q^{6} + 16q^{7} - 15q^{8} + 379q^{9} + O(q^{10}) \) \( 375q - 3q^{2} + 4q^{3} + 377q^{4} + 3q^{5} - 4q^{6} + 16q^{7} - 15q^{8} + 379q^{9} + q^{10} - 4q^{11} - 4q^{12} + 26q^{13} - 8q^{14} - 4q^{15} + 369q^{16} - q^{17} - 39q^{18} + 12q^{19} + 5q^{20} + 32q^{21} - 36q^{22} - 24q^{23} - 4q^{24} + 375q^{25} - 2q^{26} + 16q^{27} + 24q^{28} + 18q^{29} + 28q^{30} + 16q^{31} - 63q^{32} - 24q^{33} - 3q^{34} + 461q^{36} + 26q^{37} + 36q^{38} - 3q^{40} + 6q^{41} + 72q^{42} + 20q^{43} + 60q^{44} + 23q^{45} - 24q^{46} - 16q^{47} + 100q^{48} + 463q^{49} - 3q^{50} - 4q^{51} + 14q^{52} - 30q^{53} + 88q^{54} - 12q^{55} + 64q^{56} + 40q^{57} - 50q^{58} - 28q^{59} + 28q^{60} + 58q^{61} + 24q^{62} - 16q^{63} + 305q^{64} + 10q^{65} + 56q^{66} + 36q^{67} - 7q^{68} - 24q^{69} - q^{71} - 107q^{72} + 102q^{73} - 2q^{74} + 4q^{75} + 44q^{76} - 56q^{77} - 8q^{78} - 24q^{79} + 29q^{80} + 367q^{81} + 18q^{82} - 44q^{83} + 80q^{84} - q^{85} - 108q^{86} - 104q^{87} - 100q^{88} + 30q^{89} - 19q^{90} + 64q^{91} - 16q^{92} - 16q^{93} + 8q^{94} + 12q^{95} + 36q^{96} + 22q^{97} + 21q^{98} - 28q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6035))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 17 71
6035.2.a.a \(36\) \(48.190\) None \(-3\) \(-8\) \(36\) \(-7\) \(-\) \(-\) \(+\)
6035.2.a.b \(36\) \(48.190\) None \(-1\) \(-4\) \(36\) \(-7\) \(-\) \(+\) \(-\)
6035.2.a.c \(44\) \(48.190\) None \(-4\) \(-4\) \(-44\) \(-5\) \(+\) \(+\) \(+\)
6035.2.a.d \(44\) \(48.190\) None \(-2\) \(-8\) \(-44\) \(-13\) \(+\) \(-\) \(-\)
6035.2.a.e \(49\) \(48.190\) None \(1\) \(10\) \(-49\) \(15\) \(+\) \(-\) \(+\)
6035.2.a.f \(49\) \(48.190\) None \(3\) \(6\) \(-49\) \(11\) \(+\) \(+\) \(-\)
6035.2.a.g \(58\) \(48.190\) None \(1\) \(6\) \(58\) \(13\) \(-\) \(-\) \(-\)
6035.2.a.h \(59\) \(48.190\) None \(2\) \(6\) \(59\) \(9\) \(-\) \(+\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6035))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6035)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(71))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(355))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1207))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database