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Properties

Label 4003.2.a
Level $4003$
Weight $2$
Character orbit 4003.a
Rep. character $\chi_{4003}(1,\cdot)$
Character field $\Q$
Dimension $333$
Newform subspaces $3$
Sturm bound $667$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 4003 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4003.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(667\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4003))\).

Total New Old
Modular forms 334 334 0
Cusp forms 333 333 0
Eisenstein series 1 1 0

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

\(4003\)Dim
\(+\)\(154\)
\(-\)\(179\)

Trace form

\( 333 q - 2 q^{3} + 334 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{8} + 325 q^{9} + O(q^{10}) \) \( 333 q - 2 q^{3} + 334 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{8} + 325 q^{9} - 2 q^{10} + 2 q^{11} - 20 q^{12} - 4 q^{13} - 14 q^{14} + 332 q^{16} + 8 q^{17} - 16 q^{18} - 2 q^{19} - 6 q^{20} - 12 q^{21} - 6 q^{22} + 2 q^{23} - 42 q^{24} + 341 q^{25} - 4 q^{26} - 14 q^{27} - 12 q^{28} + 6 q^{29} - 40 q^{30} - 6 q^{31} + 8 q^{32} + 6 q^{33} - 14 q^{34} - 4 q^{35} + 324 q^{36} + 6 q^{37} + 14 q^{38} - 38 q^{39} - 6 q^{40} + 10 q^{41} - 40 q^{42} - 14 q^{43} - 6 q^{44} + 16 q^{45} + 18 q^{46} - 18 q^{47} - 42 q^{48} + 335 q^{49} + 14 q^{50} - 22 q^{51} - 44 q^{52} + 48 q^{53} - 18 q^{54} - 20 q^{56} - 54 q^{57} - 10 q^{58} - 14 q^{59} + 12 q^{60} + 4 q^{61} + 2 q^{62} + 10 q^{63} + 332 q^{64} + 14 q^{65} + 32 q^{66} - 2 q^{67} + 66 q^{68} + 24 q^{69} - 42 q^{70} + 12 q^{71} - 50 q^{72} + 12 q^{73} + 8 q^{74} - 32 q^{75} - 24 q^{76} + 20 q^{77} + 26 q^{78} + 20 q^{79} + 20 q^{80} + 285 q^{81} + 2 q^{82} + 6 q^{83} - 38 q^{84} + 30 q^{85} + 10 q^{86} - 8 q^{87} - 14 q^{88} + 28 q^{89} - 32 q^{90} - 14 q^{91} - 4 q^{92} + 44 q^{93} + 10 q^{94} + 44 q^{95} - 136 q^{96} - 14 q^{97} + 4 q^{98} - 34 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4003))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 4003
4003.2.a.a 4003.a 1.a $2$ $31.964$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+\beta q^{3}+\beta q^{5}+2q^{6}-q^{7}+\cdots\)
4003.2.a.b 4003.a 1.a $152$ $31.964$ None \(-22\) \(-18\) \(-59\) \(-19\) $+$ $\mathrm{SU}(2)$
4003.2.a.c 4003.a 1.a $179$ $31.964$ None \(22\) \(16\) \(61\) \(21\) $-$ $\mathrm{SU}(2)$