Properties

Label 6035.2.a
Level 6035
Weight 2
Character orbit a
Rep. character \(\chi_{6035}(1,\cdot)\)
Character field \(\Q\)
Dimension 375
Newforms 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: \(\Q\)
Newforms: \( 8 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6035))\) into irreducible Hecke orbits

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

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