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Properties

Label 4013.2.a
Level $4013$
Weight $2$
Character orbit 4013.a
Rep. character $\chi_{4013}(1,\cdot)$
Character field $\Q$
Dimension $334$
Newform subspaces $3$
Sturm bound $669$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 4013 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4013.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(669\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4013))\).

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.

\(4013\)Dim
\(+\)\(157\)
\(-\)\(177\)

Trace form

\( 334 q - 2 q^{2} + 330 q^{4} - 4 q^{5} - 2 q^{7} - 6 q^{8} + 338 q^{9} + O(q^{10}) \) \( 334 q - 2 q^{2} + 330 q^{4} - 4 q^{5} - 2 q^{7} - 6 q^{8} + 338 q^{9} - 10 q^{10} - 6 q^{11} - 2 q^{12} - 8 q^{14} - 8 q^{15} + 326 q^{16} - 12 q^{17} - 20 q^{18} - 18 q^{20} + 4 q^{21} - 2 q^{22} - 6 q^{23} - 14 q^{24} + 320 q^{25} + 18 q^{26} + 6 q^{27} - 26 q^{28} - 2 q^{29} - 24 q^{32} + 12 q^{33} - 20 q^{34} - 10 q^{35} + 318 q^{36} - 2 q^{37} + 48 q^{39} - 22 q^{40} - 10 q^{41} - 22 q^{42} + 12 q^{43} - 2 q^{44} - 30 q^{45} + 6 q^{46} - 24 q^{47} - 24 q^{48} + 324 q^{49} - 46 q^{50} + 4 q^{51} + 8 q^{52} - 30 q^{53} + 24 q^{54} - 12 q^{55} - 20 q^{56} + 28 q^{57} + 16 q^{58} + 12 q^{59} - 10 q^{60} - 4 q^{61} + 10 q^{62} - 4 q^{63} + 296 q^{64} - 10 q^{65} + 18 q^{66} - 10 q^{67} - 74 q^{68} - 10 q^{69} - 64 q^{70} + 2 q^{71} - 74 q^{72} - 4 q^{73} - 42 q^{74} - 12 q^{75} - 14 q^{76} - 56 q^{77} - 64 q^{78} - 2 q^{79} - 2 q^{80} + 382 q^{81} - 12 q^{83} + 28 q^{84} - 26 q^{85} + 14 q^{86} - 10 q^{87} - 2 q^{89} - 50 q^{90} - 16 q^{91} - 90 q^{92} - 6 q^{93} + 4 q^{94} + 12 q^{95} - 14 q^{96} + 32 q^{98} - 38 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4013))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 4013
4013.2.a.a 4013.a 1.a $1$ $32.044$ \(\Q\) None \(2\) \(-2\) \(4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-2q^{3}+2q^{4}+4q^{5}-4q^{6}+\cdots\)
4013.2.a.b 4013.a 1.a $157$ $32.044$ None \(-15\) \(-51\) \(-13\) \(-49\) $+$ $\mathrm{SU}(2)$
4013.2.a.c 4013.a 1.a $176$ $32.044$ None \(11\) \(53\) \(5\) \(46\) $-$ $\mathrm{SU}(2)$