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Properties

Label 383.2.a
Level $383$
Weight $2$
Character orbit 383.a
Rep. character $\chi_{383}(1,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $3$
Sturm bound $64$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 383 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 383.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(64\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(383))\).

Total New Old
Modular forms 33 33 0
Cusp forms 32 32 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.

\(383\)Dim
\(+\)\(8\)
\(-\)\(24\)

Trace form

\( 32 q + q^{2} + 31 q^{4} - 2 q^{6} + 6 q^{7} + 9 q^{8} + 30 q^{9} + O(q^{10}) \) \( 32 q + q^{2} + 31 q^{4} - 2 q^{6} + 6 q^{7} + 9 q^{8} + 30 q^{9} - 2 q^{10} - 2 q^{11} - 10 q^{12} + 10 q^{13} - 4 q^{14} - 8 q^{15} + 33 q^{16} + 6 q^{17} + 17 q^{18} + 6 q^{19} + 4 q^{20} - 8 q^{21} + 6 q^{22} + 6 q^{23} - 10 q^{24} + 46 q^{25} - 4 q^{26} - 12 q^{27} + 26 q^{28} - 6 q^{29} - 10 q^{30} - 4 q^{31} + 19 q^{32} + 8 q^{33} - 14 q^{34} - 12 q^{35} + 29 q^{36} + 16 q^{37} + 18 q^{38} - 12 q^{39} - 48 q^{40} - 8 q^{41} - 16 q^{42} + 16 q^{43} - 30 q^{44} - 36 q^{45} - 18 q^{46} + 2 q^{47} - 44 q^{48} + 36 q^{49} - 7 q^{50} - 24 q^{51} + 6 q^{52} - 16 q^{53} - 50 q^{54} + 24 q^{55} - 10 q^{56} + 22 q^{57} + 2 q^{58} + 18 q^{59} - 82 q^{60} + 8 q^{61} - 56 q^{62} + 22 q^{63} + 21 q^{64} + 16 q^{65} - 34 q^{66} + 28 q^{67} - 8 q^{68} - 12 q^{69} - 54 q^{70} + 6 q^{71} + 47 q^{72} + 40 q^{73} - 14 q^{74} - 46 q^{75} + 28 q^{76} - 18 q^{77} - 24 q^{78} + 2 q^{79} - 66 q^{80} + 24 q^{81} - 24 q^{83} - 152 q^{84} + 44 q^{85} + 6 q^{86} + 30 q^{87} - 32 q^{88} - 44 q^{89} - 116 q^{90} + 14 q^{91} - 50 q^{92} + 18 q^{93} - 70 q^{94} - 64 q^{95} - 79 q^{96} + 36 q^{97} - 22 q^{98} - 52 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(383))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 383
383.2.a.a 383.a 1.a $2$ $3.058$ \(\Q(\sqrt{5}) \) None \(-1\) \(-3\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1-\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
383.2.a.b 383.a 1.a $6$ $3.058$ 6.6.3151861.1 None \(-3\) \(1\) \(-4\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}+\beta _{4})q^{2}+\beta _{1}q^{3}+(-\beta _{4}+\beta _{5})q^{4}+\cdots\)
383.2.a.c 383.a 1.a $24$ $3.058$ None \(5\) \(2\) \(3\) \(17\) $-$ $\mathrm{SU}(2)$