Properties

Label 8007.2.a
Level 8007
Weight 2
Character orbit a
Rep. character \(\chi_{8007}(1,\cdot)\)
Character field \(\Q\)
Dimension 415
Newforms 10
Sturm bound 1896
Trace bound 2

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Defining parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)
Character field: \(\Q\)
Newforms: \( 10 \)
Sturm bound: \(1896\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8007))\).

Total New Old
Modular forms 952 415 537
Cusp forms 945 415 530
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(17\)\(157\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(48\)
\(+\)\(+\)\(-\)\(-\)\(56\)
\(+\)\(-\)\(+\)\(-\)\(64\)
\(+\)\(-\)\(-\)\(+\)\(40\)
\(-\)\(+\)\(+\)\(-\)\(56\)
\(-\)\(+\)\(-\)\(+\)\(48\)
\(-\)\(-\)\(+\)\(+\)\(40\)
\(-\)\(-\)\(-\)\(-\)\(63\)
Plus space\(+\)\(176\)
Minus space\(-\)\(239\)

Trace form

\( 415q + 5q^{2} - q^{3} + 417q^{4} - 6q^{5} + q^{6} + 8q^{7} + 9q^{8} + 415q^{9} + O(q^{10}) \) \( 415q + 5q^{2} - q^{3} + 417q^{4} - 6q^{5} + q^{6} + 8q^{7} + 9q^{8} + 415q^{9} - 10q^{10} + 4q^{11} - 7q^{12} - 14q^{13} - 16q^{14} + 2q^{15} + 409q^{16} - q^{17} + 5q^{18} - 20q^{19} - 2q^{20} - 8q^{21} + 36q^{22} + 24q^{23} - 3q^{24} + 425q^{25} + 14q^{26} - q^{27} - 8q^{28} + 18q^{29} - 18q^{30} - 8q^{31} + 33q^{32} + 12q^{33} + 5q^{34} + 8q^{35} + 417q^{36} + 18q^{37} - 28q^{38} - 14q^{39} + 14q^{40} - 10q^{41} + 24q^{42} + 12q^{43} + 12q^{44} - 6q^{45} + 32q^{46} - 31q^{48} + 383q^{49} + 19q^{50} - q^{51} - 58q^{52} + 26q^{53} + q^{54} - 8q^{55} - 48q^{56} - 20q^{57} - 2q^{58} - 4q^{59} + 70q^{60} - 14q^{61} - 8q^{62} + 8q^{63} + 465q^{64} + 44q^{65} - 12q^{66} - 52q^{67} - 7q^{68} - 24q^{69} + 48q^{70} - 16q^{71} + 9q^{72} - 10q^{73} - 18q^{74} - 31q^{75} - 76q^{76} + 40q^{77} + 14q^{78} + 32q^{79} - 106q^{80} + 415q^{81} - 38q^{82} + 44q^{83} - 32q^{84} + 2q^{85} + 68q^{86} - 6q^{87} + 100q^{88} + 22q^{89} - 10q^{90} - 56q^{91} + 160q^{92} - 32q^{93} - 16q^{94} + 88q^{95} + 5q^{96} + 102q^{97} + 101q^{98} + 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8007))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 17 157
8007.2.a.a \(1\) \(63.936\) \(\Q\) None \(1\) \(-1\) \(0\) \(2\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}-q^{4}-q^{6}+2q^{7}-3q^{8}+\cdots\)
8007.2.a.b \(2\) \(63.936\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-4\) \(-4\) \(-\) \(+\) \(-\) \(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots\)
8007.2.a.c \(39\) \(63.936\) None \(-4\) \(-39\) \(-3\) \(-5\) \(+\) \(-\) \(-\)
8007.2.a.d \(40\) \(63.936\) None \(-7\) \(40\) \(-15\) \(-13\) \(-\) \(-\) \(+\)
8007.2.a.e \(46\) \(63.936\) None \(-5\) \(46\) \(-19\) \(1\) \(-\) \(+\) \(-\)
8007.2.a.f \(48\) \(63.936\) None \(-1\) \(-48\) \(1\) \(-13\) \(+\) \(+\) \(+\)
8007.2.a.g \(56\) \(63.936\) None \(1\) \(-56\) \(1\) \(19\) \(+\) \(+\) \(-\)
8007.2.a.h \(56\) \(63.936\) None \(7\) \(56\) \(17\) \(5\) \(-\) \(+\) \(+\)
8007.2.a.i \(63\) \(63.936\) None \(10\) \(63\) \(19\) \(11\) \(-\) \(-\) \(-\)
8007.2.a.j \(64\) \(63.936\) None \(5\) \(-64\) \(-3\) \(5\) \(+\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8007))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8007)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(157))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(471))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2669))\)\(^{\oplus 2}\)