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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 53 151
8003.2.a.a 8003.a 1.a $147$ $63.904$ None \(-6\) \(-23\) \(-25\) \(-33\) $-$ $-$ $\mathrm{SU}(2)$
8003.2.a.b 8003.a 1.a $153$ $63.904$ None \(-9\) \(-17\) \(-31\) \(-17\) $+$ $+$ $\mathrm{SU}(2)$
8003.2.a.c 8003.a 1.a $172$ $63.904$ None \(8\) \(25\) \(27\) \(31\) $+$ $-$ $\mathrm{SU}(2)$
8003.2.a.d 8003.a 1.a $179$ $63.904$ None \(8\) \(15\) \(27\) \(23\) $-$ $+$ $\mathrm{SU}(2)$

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

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