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Properties

Label 4021.2.a
Level $4021$
Weight $2$
Character orbit 4021.a
Rep. character $\chi_{4021}(1,\cdot)$
Character field $\Q$
Dimension $334$
Newform subspaces $3$
Sturm bound $670$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 4021 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4021.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(670\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4021))\).

Total New Old
Modular forms 335 335 0
Cusp forms 334 334 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.

\(4021\)Dim
\(+\)\(152\)
\(-\)\(182\)

Trace form

\( 334 q + 330 q^{4} - 2 q^{5} - 2 q^{6} + 6 q^{8} + 334 q^{9} + O(q^{10}) \) \( 334 q + 330 q^{4} - 2 q^{5} - 2 q^{6} + 6 q^{8} + 334 q^{9} - 6 q^{10} + 10 q^{11} + 2 q^{12} - 12 q^{13} + 6 q^{14} - 6 q^{15} + 326 q^{16} - 8 q^{17} - 8 q^{18} - 6 q^{19} - 2 q^{20} - 24 q^{21} + 16 q^{22} + 2 q^{23} + 2 q^{24} + 336 q^{25} + 8 q^{26} + 6 q^{27} - 4 q^{28} - 4 q^{29} + 2 q^{31} + 22 q^{32} + 6 q^{33} - 8 q^{34} + 14 q^{35} + 354 q^{36} - 4 q^{37} - 12 q^{38} - 8 q^{39} - 50 q^{40} + 8 q^{41} + 28 q^{42} - 2 q^{43} + 46 q^{44} - 4 q^{45} - 28 q^{46} - 2 q^{47} - 10 q^{48} + 328 q^{49} + 6 q^{50} + 8 q^{51} - 42 q^{52} - 8 q^{53} + 14 q^{54} - 6 q^{55} + 32 q^{56} - 22 q^{57} - 28 q^{58} + 40 q^{59} - 64 q^{60} - 42 q^{61} - 16 q^{62} - 38 q^{63} + 314 q^{64} - 34 q^{65} - 6 q^{66} - 10 q^{67} - 26 q^{68} - 32 q^{69} - 14 q^{70} - 8 q^{71} - 2 q^{72} - 22 q^{74} - 42 q^{75} - 60 q^{76} - 6 q^{77} - 52 q^{78} + 16 q^{79} - 36 q^{80} + 310 q^{81} - 36 q^{82} + 18 q^{83} - 136 q^{84} + 6 q^{85} - 34 q^{86} - 24 q^{87} - 10 q^{88} - 38 q^{89} - 130 q^{90} - 16 q^{91} - 36 q^{94} + 10 q^{95} - 14 q^{96} + 6 q^{97} - 8 q^{98} + 100 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4021))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 4021
4021.2.a.a 4021.a 1.a $1$ $32.108$ \(\Q\) None \(-2\) \(1\) \(3\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}+3q^{5}-2q^{6}+\cdots\)
4021.2.a.b 4021.a 1.a $151$ $32.108$ None \(-16\) \(-29\) \(-27\) \(-18\) $+$ $\mathrm{SU}(2)$
4021.2.a.c 4021.a 1.a $182$ $32.108$ None \(18\) \(28\) \(22\) \(14\) $-$ $\mathrm{SU}(2)$