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Properties

Label 6043.2.a
Level $6043$
Weight $2$
Character orbit 6043.a
Rep. character $\chi_{6043}(1,\cdot)$
Character field $\Q$
Dimension $503$
Newform subspaces $3$
Sturm bound $1007$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 6043 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6043.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(1007\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6043))\).

Total New Old
Modular forms 504 504 0
Cusp forms 503 503 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.

\(6043\)Dim
\(+\)\(243\)
\(-\)\(260\)

Trace form

\( 503 q - 2 q^{2} - 4 q^{3} + 502 q^{4} - 2 q^{5} - 4 q^{7} + 497 q^{9} + O(q^{10}) \) \( 503 q - 2 q^{2} - 4 q^{3} + 502 q^{4} - 2 q^{5} - 4 q^{7} + 497 q^{9} + 12 q^{10} - 4 q^{11} - 14 q^{12} - 6 q^{13} - 2 q^{14} - 4 q^{15} + 504 q^{16} - 4 q^{17} - 12 q^{18} - 6 q^{19} - 8 q^{20} - 10 q^{21} + 8 q^{22} + 6 q^{23} - 2 q^{24} + 511 q^{25} + 36 q^{26} - 4 q^{27} - 16 q^{28} - 6 q^{29} - 20 q^{30} - 10 q^{31} - 12 q^{32} - 2 q^{33} + 4 q^{34} + 2 q^{35} + 494 q^{36} - 2 q^{37} + 4 q^{38} + 20 q^{39} + 30 q^{40} + 2 q^{41} - 4 q^{42} - 22 q^{43} - 18 q^{44} - 22 q^{45} - 26 q^{46} - 44 q^{48} + 483 q^{49} + 20 q^{50} - 8 q^{51} - 20 q^{52} + 6 q^{53} + 16 q^{54} - 22 q^{55} + 30 q^{56} + 8 q^{57} + 8 q^{58} - 12 q^{59} - 50 q^{60} - 6 q^{61} + 8 q^{62} - 30 q^{63} + 528 q^{64} + 46 q^{65} + 26 q^{66} - 48 q^{67} + 14 q^{68} - 24 q^{70} - 14 q^{71} - 46 q^{72} - 10 q^{73} - 54 q^{75} + 10 q^{76} - 16 q^{77} - 42 q^{78} - 12 q^{79} - 26 q^{80} + 479 q^{81} + 14 q^{82} - 6 q^{83} - 96 q^{84} + 16 q^{85} - 2 q^{86} - 14 q^{87} - 46 q^{88} + 16 q^{89} + 44 q^{90} - 8 q^{91} + 64 q^{92} + 28 q^{93} + 50 q^{94} + 12 q^{95} + 4 q^{96} + 12 q^{97} - 30 q^{98} - 42 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6043))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 6043
6043.2.a.a 6043.a 1.a $1$ $48.254$ \(\Q\) None \(-1\) \(-2\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}-q^{4}+2q^{6}-2q^{7}+3q^{8}+\cdots\)
6043.2.a.b 6043.a 1.a $243$ $48.254$ None \(-40\) \(-27\) \(-85\) \(-28\) $+$ $\mathrm{SU}(2)$
6043.2.a.c 6043.a 1.a $259$ $48.254$ None \(39\) \(25\) \(83\) \(26\) $-$ $\mathrm{SU}(2)$