Properties

Label 8003.2.a
Level $8003$
Weight $2$
Character orbit 8003.a
Rep. character $\chi_{8003}(1,\cdot)$
Character field $\Q$
Dimension $651$
Newform subspaces $4$
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: \(\Q\)
Newform subspaces: \( 4 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8003))\) into newform subspaces

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database