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

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

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

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