Properties

Label 3017.2.a
Level 3017
Weight 2
Character orbit a
Rep. character \(\chi_{3017}(1,\cdot)\)
Character field \(\Q\)
Dimension 215
Newforms 6
Sturm bound 576
Trace bound 2

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Defining parameters

Level: \( N \) = \( 3017 = 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3017.a (trivial)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(576\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3017))\).

Total New Old
Modular forms 290 215 75
Cusp forms 287 215 72
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.

\(7\)\(431\)FrickeDim.
\(+\)\(+\)\(+\)\(58\)
\(+\)\(-\)\(-\)\(49\)
\(-\)\(+\)\(-\)\(70\)
\(-\)\(-\)\(+\)\(38\)
Plus space\(+\)\(96\)
Minus space\(-\)\(119\)

Trace form

\( 215q - q^{2} - 4q^{3} + 211q^{4} - 6q^{5} - 12q^{6} + q^{7} - 9q^{8} + 207q^{9} + O(q^{10}) \) \( 215q - q^{2} - 4q^{3} + 211q^{4} - 6q^{5} - 12q^{6} + q^{7} - 9q^{8} + 207q^{9} - 2q^{10} - 12q^{12} - 2q^{13} + 3q^{14} - 4q^{15} + 215q^{16} - 10q^{17} + 7q^{18} - 8q^{19} + 6q^{20} + 4q^{21} + 20q^{22} - 4q^{23} - 32q^{24} + 201q^{25} - 22q^{26} - 28q^{27} + 7q^{28} - 2q^{29} - 12q^{30} - 28q^{31} - 9q^{32} - 28q^{33} - 34q^{34} + 2q^{35} + 151q^{36} - 14q^{37} - 4q^{38} + 16q^{39} - 22q^{40} - 14q^{41} - 8q^{42} + 16q^{43} - 8q^{44} - 62q^{45} - 24q^{46} - 16q^{47} - 12q^{48} + 215q^{49} + q^{50} - 4q^{51} - 14q^{52} - 14q^{53} - 68q^{54} + 28q^{55} + 15q^{56} - 12q^{57} - 46q^{58} - 4q^{59} + 68q^{60} - 38q^{61} + 36q^{62} + 13q^{63} + 211q^{64} - 20q^{65} - 36q^{66} + 28q^{67} - 18q^{68} - 20q^{69} + 18q^{70} + 16q^{71} + 3q^{72} - 42q^{73} + 62q^{74} + 20q^{75} - 32q^{76} + 4q^{77} + 56q^{78} + 28q^{79} - 30q^{80} + 223q^{81} - 30q^{82} + 68q^{83} + 28q^{84} - 20q^{85} - 48q^{86} + 48q^{87} + 100q^{88} - 50q^{89} + 158q^{90} + 6q^{91} + 48q^{92} - 40q^{93} - 32q^{94} + 32q^{95} - 80q^{96} - 38q^{97} - q^{98} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3017))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 431
3017.2.a.a \(1\) \(24.091\) \(\Q\) None \(-1\) \(1\) \(2\) \(1\) \(-\) \(-\) \(q-q^{2}+q^{3}-q^{4}+2q^{5}-q^{6}+q^{7}+\cdots\)
3017.2.a.b \(1\) \(24.091\) \(\Q\) None \(1\) \(1\) \(-1\) \(-1\) \(+\) \(-\) \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
3017.2.a.c \(37\) \(24.091\) None \(-4\) \(-9\) \(-7\) \(37\) \(-\) \(-\)
3017.2.a.d \(48\) \(24.091\) None \(1\) \(7\) \(6\) \(-48\) \(+\) \(-\)
3017.2.a.e \(58\) \(24.091\) None \(-4\) \(-12\) \(-9\) \(-58\) \(+\) \(+\)
3017.2.a.f \(70\) \(24.091\) None \(6\) \(8\) \(3\) \(70\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3017))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3017)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(431))\)\(^{\oplus 2}\)