Properties

Label 8027.2.a
Level 8027
Weight 2
Character orbit a
Rep. character \(\chi_{8027}(1,\cdot)\)
Character field \(\Q\)
Dimension 639
Newforms 6
Sturm bound 1400
Trace bound 2

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Defining parameters

Level: \( N \) = \( 8027 = 23 \cdot 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8027.a (trivial)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(1400\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8027))\).

Total New Old
Modular forms 702 639 63
Cusp forms 699 639 60
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.

\(23\)\(349\)FrickeDim.
\(+\)\(+\)\(+\)\(149\)
\(+\)\(-\)\(-\)\(170\)
\(-\)\(+\)\(-\)\(177\)
\(-\)\(-\)\(+\)\(143\)
Plus space\(+\)\(292\)
Minus space\(-\)\(347\)

Trace form

\( 639q + q^{2} + 645q^{4} + 6q^{5} + 4q^{6} + 9q^{8} + 631q^{9} + O(q^{10}) \) \( 639q + q^{2} + 645q^{4} + 6q^{5} + 4q^{6} + 9q^{8} + 631q^{9} - 6q^{10} - 20q^{12} + 10q^{13} - 20q^{14} - 4q^{15} + 637q^{16} - 14q^{17} - 19q^{18} + 8q^{19} - 2q^{20} + 12q^{21} - 8q^{22} + q^{23} - 12q^{24} + 645q^{25} + 26q^{26} + 12q^{27} + 32q^{28} + 14q^{29} - 12q^{30} + 24q^{31} - 31q^{32} - 36q^{33} + 6q^{34} + 629q^{36} + 38q^{37} - 20q^{39} + 18q^{40} + 10q^{41} - 16q^{42} - 4q^{43} - 40q^{44} + 26q^{45} - q^{46} - 12q^{47} - 48q^{48} + 655q^{49} + 31q^{50} - 60q^{51} + 50q^{52} - 14q^{53} - 56q^{54} - 36q^{55} - 48q^{56} + 8q^{57} + 54q^{58} - 52q^{59} - 60q^{60} + 34q^{61} - 8q^{62} - 68q^{63} + 701q^{64} + 28q^{65} + 8q^{66} + 24q^{67} + 6q^{68} + 4q^{69} + 88q^{70} - 92q^{71} - 15q^{72} + 2q^{73} + 2q^{74} - 96q^{75} + 64q^{76} + 24q^{77} + 20q^{78} + 24q^{79} + 22q^{80} + 647q^{81} + 42q^{82} - 12q^{83} - 52q^{84} + 56q^{85} + 32q^{86} - 44q^{87} - 60q^{88} + 18q^{89} + 34q^{90} + 40q^{91} + 7q^{92} + 108q^{93} + 64q^{94} + 8q^{95} + 4q^{96} + 2q^{97} - 15q^{98} - 36q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8027))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 23 349
8027.2.a.a \(1\) \(64.096\) \(\Q\) None \(-2\) \(-3\) \(0\) \(-1\) \(-\) \(+\) \(q-2q^{2}-3q^{3}+2q^{4}+6q^{6}-q^{7}+\cdots\)
8027.2.a.b \(1\) \(64.096\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(q+q^{3}-2q^{4}-q^{7}-2q^{9}+3q^{11}+\cdots\)
8027.2.a.c \(143\) \(64.096\) None \(-17\) \(-17\) \(-22\) \(-33\) \(-\) \(-\)
8027.2.a.d \(149\) \(64.096\) None \(-5\) \(-5\) \(-28\) \(-33\) \(+\) \(+\)
8027.2.a.e \(169\) \(64.096\) None \(6\) \(2\) \(28\) \(38\) \(+\) \(-\)
8027.2.a.f \(176\) \(64.096\) None \(19\) \(22\) \(28\) \(30\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8027))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8027)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(349))\)\(^{\oplus 2}\)