Properties

Label 8002.2.a
Level 8002
Weight 2
Character orbit a
Rep. character \(\chi_{8002}(1,\cdot)\)
Character field \(\Q\)
Dimension 333
Newforms 7
Sturm bound 2001
Trace bound 3

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Defining parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)
Character field: \(\Q\)
Newforms: \( 7 \)
Sturm bound: \(2001\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8002))\).

Total New Old
Modular forms 1002 333 669
Cusp forms 999 333 666
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.

\(2\)\(4001\)FrickeDim.
\(+\)\(+\)\(+\)\(89\)
\(+\)\(-\)\(-\)\(77\)
\(-\)\(+\)\(-\)\(95\)
\(-\)\(-\)\(+\)\(72\)
Plus space\(+\)\(161\)
Minus space\(-\)\(172\)

Trace form

\(333q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 333q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut 337q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(333q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 333q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut 337q^{9} \) \(\mathstrut +\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 6q^{11} \) \(\mathstrut -\mathstrut 2q^{12} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 333q^{16} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 2q^{20} \) \(\mathstrut +\mathstrut 8q^{21} \) \(\mathstrut -\mathstrut 2q^{22} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 2q^{24} \) \(\mathstrut +\mathstrut 331q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 4q^{28} \) \(\mathstrut +\mathstrut 18q^{29} \) \(\mathstrut +\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 24q^{31} \) \(\mathstrut +\mathstrut q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut +\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 337q^{36} \) \(\mathstrut -\mathstrut 16q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut +\mathstrut 2q^{40} \) \(\mathstrut +\mathstrut 2q^{41} \) \(\mathstrut +\mathstrut 6q^{43} \) \(\mathstrut +\mathstrut 6q^{44} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 8q^{46} \) \(\mathstrut -\mathstrut 12q^{47} \) \(\mathstrut -\mathstrut 2q^{48} \) \(\mathstrut +\mathstrut 337q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut +\mathstrut 28q^{51} \) \(\mathstrut +\mathstrut 2q^{52} \) \(\mathstrut +\mathstrut 4q^{53} \) \(\mathstrut +\mathstrut 20q^{54} \) \(\mathstrut -\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 8q^{56} \) \(\mathstrut -\mathstrut 12q^{57} \) \(\mathstrut -\mathstrut 6q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut 8q^{62} \) \(\mathstrut -\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 333q^{64} \) \(\mathstrut +\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut -\mathstrut 10q^{67} \) \(\mathstrut +\mathstrut 6q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut -\mathstrut 4q^{71} \) \(\mathstrut +\mathstrut 5q^{72} \) \(\mathstrut -\mathstrut 6q^{73} \) \(\mathstrut +\mathstrut 20q^{74} \) \(\mathstrut -\mathstrut 54q^{75} \) \(\mathstrut -\mathstrut 36q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 2q^{80} \) \(\mathstrut +\mathstrut 333q^{81} \) \(\mathstrut +\mathstrut 6q^{82} \) \(\mathstrut -\mathstrut 32q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 36q^{85} \) \(\mathstrut -\mathstrut 6q^{86} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 2q^{88} \) \(\mathstrut +\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 4q^{91} \) \(\mathstrut +\mathstrut 8q^{92} \) \(\mathstrut -\mathstrut 44q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut +\mathstrut 2q^{96} \) \(\mathstrut +\mathstrut 14q^{97} \) \(\mathstrut +\mathstrut 25q^{98} \) \(\mathstrut +\mathstrut 38q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8002))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 4001
8002.2.a.a \(1\) \(63.896\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
8002.2.a.b \(1\) \(63.896\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{8}-3q^{9}-2q^{11}+4q^{13}+\cdots\)
8002.2.a.c \(1\) \(63.896\) \(\Q\) None \(1\) \(2\) \(-2\) \(0\) \(-\) \(-\) \(q+q^{2}+2q^{3}+q^{4}-2q^{5}+2q^{6}+q^{8}+\cdots\)
8002.2.a.d \(69\) \(63.896\) None \(69\) \(-25\) \(-33\) \(-19\) \(-\) \(-\)
8002.2.a.e \(77\) \(63.896\) None \(-77\) \(10\) \(18\) \(21\) \(+\) \(-\)
8002.2.a.f \(89\) \(63.896\) None \(-89\) \(-12\) \(-18\) \(-27\) \(+\) \(+\)
8002.2.a.g \(95\) \(63.896\) None \(95\) \(24\) \(36\) \(21\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8002))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8002)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(4001))\)\(^{\oplus 2}\)