Properties

Label 8014.2.a
Level 8014
Weight 2
Character orbit a
Rep. character \(\chi_{8014}(1,\cdot)\)
Character field \(\Q\)
Dimension 333
Newforms 5
Sturm bound 2004
Trace bound 2

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Defining parameters

Level: \( N \) = \( 8014 = 2 \cdot 4007 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8014.a (trivial)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(2004\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8014))\).

Total New Old
Modular forms 1004 333 671
Cusp forms 1001 333 668
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.

\(2\)\(4007\)FrickeDim.
\(+\)\(+\)\(+\)\(76\)
\(+\)\(-\)\(-\)\(91\)
\(-\)\(+\)\(-\)\(90\)
\(-\)\(-\)\(+\)\(76\)
Plus space\(+\)\(152\)
Minus space\(-\)\(181\)

Trace form

\(333q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 333q^{4} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut 337q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(333q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 333q^{4} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut 337q^{9} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 6q^{11} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 333q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 10q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 327q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 4q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 16q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut +\mathstrut 28q^{33} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 337q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 2q^{41} \) \(\mathstrut +\mathstrut 12q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 6q^{44} \) \(\mathstrut +\mathstrut 8q^{45} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 345q^{49} \) \(\mathstrut -\mathstrut 7q^{50} \) \(\mathstrut -\mathstrut 16q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 16q^{55} \) \(\mathstrut -\mathstrut 36q^{57} \) \(\mathstrut -\mathstrut 10q^{58} \) \(\mathstrut -\mathstrut 20q^{59} \) \(\mathstrut -\mathstrut 10q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 24q^{63} \) \(\mathstrut +\mathstrut 333q^{64} \) \(\mathstrut -\mathstrut 52q^{65} \) \(\mathstrut +\mathstrut 32q^{66} \) \(\mathstrut -\mathstrut 30q^{67} \) \(\mathstrut -\mathstrut 6q^{68} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 8q^{70} \) \(\mathstrut -\mathstrut 5q^{72} \) \(\mathstrut -\mathstrut 6q^{73} \) \(\mathstrut +\mathstrut 2q^{74} \) \(\mathstrut -\mathstrut 44q^{75} \) \(\mathstrut -\mathstrut 2q^{76} \) \(\mathstrut -\mathstrut 32q^{77} \) \(\mathstrut -\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 4q^{79} \) \(\mathstrut +\mathstrut 4q^{80} \) \(\mathstrut +\mathstrut 333q^{81} \) \(\mathstrut -\mathstrut 6q^{82} \) \(\mathstrut -\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 4q^{84} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut -\mathstrut 4q^{86} \) \(\mathstrut -\mathstrut 64q^{87} \) \(\mathstrut -\mathstrut 10q^{88} \) \(\mathstrut +\mathstrut 6q^{89} \) \(\mathstrut -\mathstrut 36q^{90} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut +\mathstrut 4q^{92} \) \(\mathstrut -\mathstrut 24q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 7q^{98} \) \(\mathstrut +\mathstrut 38q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8014))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 4007
8014.2.a.a \(2\) \(63.992\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(1\) \(-1\) \(-\) \(+\) \(q+q^{2}-2\beta q^{3}+q^{4}+\beta q^{5}-2\beta q^{6}+\cdots\)
8014.2.a.b \(76\) \(63.992\) None \(-76\) \(2\) \(-18\) \(12\) \(+\) \(+\)
8014.2.a.c \(76\) \(63.992\) None \(76\) \(-20\) \(-26\) \(-34\) \(-\) \(-\)
8014.2.a.d \(88\) \(63.992\) None \(88\) \(22\) \(25\) \(33\) \(-\) \(+\)
8014.2.a.e \(91\) \(63.992\) None \(-91\) \(-2\) \(22\) \(-14\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8014))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8014)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(4007))\)\(^{\oplus 2}\)