Properties

Label 4027.2.a
Level $4027$
Weight $2$
Character orbit 4027.a
Rep. character $\chi_{4027}(1,\cdot)$
Character field $\Q$
Dimension $335$
Newform subspaces $3$
Sturm bound $671$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 4027 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4027.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(671\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4027))\).

Total New Old
Modular forms 336 336 0
Cusp forms 335 335 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.

\(4027\)Dim
\(+\)\(159\)
\(-\)\(176\)

Trace form

\( 335 q - 2 q^{2} - 4 q^{3} + 334 q^{4} - 6 q^{6} - 2 q^{7} - 12 q^{8} + 329 q^{9} + O(q^{10}) \) \( 335 q - 2 q^{2} - 4 q^{3} + 334 q^{4} - 6 q^{6} - 2 q^{7} - 12 q^{8} + 329 q^{9} - 2 q^{10} - 28 q^{12} - 2 q^{13} - 4 q^{14} - 4 q^{15} + 328 q^{16} + 4 q^{17} - 4 q^{18} - 2 q^{19} + 8 q^{20} - 10 q^{21} - 8 q^{22} + 6 q^{23} - 28 q^{24} + 341 q^{25} + 8 q^{26} - 28 q^{27} - 10 q^{28} + 4 q^{29} - 14 q^{30} - 10 q^{31} - 26 q^{32} + 10 q^{33} + 18 q^{34} - 6 q^{35} + 284 q^{36} + 2 q^{37} + 8 q^{38} - 4 q^{39} + 10 q^{40} + 16 q^{41} - 60 q^{42} - 30 q^{43} - 8 q^{44} - 2 q^{45} - 26 q^{46} - 12 q^{47} - 94 q^{48} + 341 q^{49} - 22 q^{50} - 22 q^{51} - 52 q^{52} + 2 q^{53} - 72 q^{54} + 2 q^{55} - 36 q^{56} - 4 q^{57} - 4 q^{58} + 2 q^{59} - 60 q^{60} + 6 q^{61} + 24 q^{62} - 14 q^{63} + 308 q^{64} + 50 q^{65} - 24 q^{66} - 54 q^{67} + 16 q^{68} + 18 q^{69} - 40 q^{70} + 32 q^{71} - 48 q^{72} + 2 q^{73} - 26 q^{74} - 52 q^{75} - 10 q^{76} + 46 q^{77} - 6 q^{79} + 18 q^{80} + 303 q^{81} - 30 q^{82} + 32 q^{83} - 46 q^{84} + 60 q^{85} - 36 q^{86} - 12 q^{87} - 72 q^{88} + 18 q^{89} + 10 q^{90} - 40 q^{91} - 12 q^{92} + 14 q^{93} + 26 q^{94} - 32 q^{95} - 64 q^{96} + 14 q^{97} + 14 q^{98} - 14 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4027))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 4027
4027.2.a.a 4027.a 1.a $2$ $32.156$ \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(-2\) \(-7\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-2+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
4027.2.a.b 4027.a 1.a $159$ $32.156$ None \(-22\) \(-19\) \(-70\) \(-19\) $+$ $\mathrm{SU}(2)$
4027.2.a.c 4027.a 1.a $174$ $32.156$ None \(21\) \(17\) \(72\) \(24\) $-$ $\mathrm{SU}(2)$