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

Related objects

Downloads

Learn more about

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

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

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

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