Properties

Label 8003.2.a
Level 8003
Weight 2
Character orbit a
Rep. character \(\chi_{8003}(1,\cdot)\)
Character field \(\Q\)
Dimension 651
Newforms 4
Sturm bound 1368
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8003 = 53 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8003.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(1368\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8003))\).

Total New Old
Modular forms 686 651 35
Cusp forms 683 651 32
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.

\(53\)\(151\)FrickeDim.
\(+\)\(+\)\(+\)\(153\)
\(+\)\(-\)\(-\)\(172\)
\(-\)\(+\)\(-\)\(179\)
\(-\)\(-\)\(+\)\(147\)
Plus space\(+\)\(300\)
Minus space\(-\)\(351\)

Trace form

\(651q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 657q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 643q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(651q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 657q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 643q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 14q^{13} \) \(\mathstrut -\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 24q^{15} \) \(\mathstrut +\mathstrut 649q^{16} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 29q^{18} \) \(\mathstrut -\mathstrut 14q^{20} \) \(\mathstrut -\mathstrut 8q^{21} \) \(\mathstrut -\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 24q^{24} \) \(\mathstrut +\mathstrut 661q^{25} \) \(\mathstrut -\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 24q^{27} \) \(\mathstrut +\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 32q^{30} \) \(\mathstrut +\mathstrut 12q^{31} \) \(\mathstrut -\mathstrut 15q^{32} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 689q^{36} \) \(\mathstrut +\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 34q^{38} \) \(\mathstrut +\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 16q^{40} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 36q^{43} \) \(\mathstrut -\mathstrut 38q^{44} \) \(\mathstrut +\mathstrut 22q^{45} \) \(\mathstrut -\mathstrut 8q^{46} \) \(\mathstrut -\mathstrut 32q^{48} \) \(\mathstrut +\mathstrut 663q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut +\mathstrut 40q^{51} \) \(\mathstrut +\mathstrut 42q^{52} \) \(\mathstrut +\mathstrut q^{53} \) \(\mathstrut -\mathstrut 104q^{54} \) \(\mathstrut -\mathstrut 24q^{55} \) \(\mathstrut -\mathstrut 52q^{56} \) \(\mathstrut +\mathstrut 24q^{57} \) \(\mathstrut +\mathstrut 16q^{58} \) \(\mathstrut -\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 68q^{60} \) \(\mathstrut +\mathstrut 26q^{61} \) \(\mathstrut -\mathstrut 36q^{62} \) \(\mathstrut +\mathstrut 56q^{63} \) \(\mathstrut +\mathstrut 653q^{64} \) \(\mathstrut +\mathstrut 36q^{65} \) \(\mathstrut -\mathstrut 20q^{66} \) \(\mathstrut +\mathstrut 16q^{67} \) \(\mathstrut -\mathstrut 4q^{68} \) \(\mathstrut +\mathstrut 28q^{69} \) \(\mathstrut -\mathstrut 56q^{70} \) \(\mathstrut +\mathstrut 24q^{71} \) \(\mathstrut -\mathstrut 55q^{72} \) \(\mathstrut +\mathstrut 10q^{73} \) \(\mathstrut -\mathstrut 78q^{74} \) \(\mathstrut -\mathstrut 36q^{75} \) \(\mathstrut -\mathstrut 8q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 28q^{78} \) \(\mathstrut +\mathstrut 64q^{79} \) \(\mathstrut -\mathstrut 56q^{80} \) \(\mathstrut +\mathstrut 579q^{81} \) \(\mathstrut -\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 44q^{83} \) \(\mathstrut -\mathstrut 36q^{84} \) \(\mathstrut -\mathstrut 48q^{85} \) \(\mathstrut +\mathstrut 4q^{86} \) \(\mathstrut -\mathstrut 80q^{88} \) \(\mathstrut -\mathstrut 26q^{89} \) \(\mathstrut -\mathstrut 82q^{90} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 48q^{92} \) \(\mathstrut +\mathstrut 20q^{93} \) \(\mathstrut -\mathstrut 30q^{94} \) \(\mathstrut -\mathstrut 28q^{95} \) \(\mathstrut +\mathstrut 24q^{96} \) \(\mathstrut +\mathstrut 6q^{97} \) \(\mathstrut -\mathstrut 39q^{98} \) \(\mathstrut +\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8003))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 53 151
8003.2.a.a \(147\) \(63.904\) None \(-6\) \(-23\) \(-25\) \(-33\) \(-\) \(-\)
8003.2.a.b \(153\) \(63.904\) None \(-9\) \(-17\) \(-31\) \(-17\) \(+\) \(+\)
8003.2.a.c \(172\) \(63.904\) None \(8\) \(25\) \(27\) \(31\) \(+\) \(-\)
8003.2.a.d \(179\) \(63.904\) None \(8\) \(15\) \(27\) \(23\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8003))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8003)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(53))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(151))\)\(^{\oplus 2}\)