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Properties

Label 3019.2.a
Level $3019$
Weight $2$
Character orbit 3019.a
Rep. character $\chi_{3019}(1,\cdot)$
Character field $\Q$
Dimension $251$
Newform subspaces $3$
Sturm bound $503$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 3019 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3019.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(503\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3019))\).

Total New Old
Modular forms 252 252 0
Cusp forms 251 251 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.

\(3019\)Dim
\(+\)\(119\)
\(-\)\(132\)

Trace form

\( 251 q - 2 q^{2} - 4 q^{3} + 246 q^{4} - 6 q^{6} - 4 q^{7} - 6 q^{8} + 245 q^{9} + O(q^{10}) \) \( 251 q - 2 q^{2} - 4 q^{3} + 246 q^{4} - 6 q^{6} - 4 q^{7} - 6 q^{8} + 245 q^{9} - 2 q^{10} - 12 q^{11} - 18 q^{12} + 4 q^{14} - 2 q^{15} + 224 q^{16} - 16 q^{18} - 16 q^{19} - 10 q^{20} - 6 q^{21} + 4 q^{22} - 12 q^{23} - 20 q^{24} + 259 q^{25} - 22 q^{26} - 34 q^{27} - 10 q^{28} - 6 q^{29} - 12 q^{30} - 6 q^{31} - 4 q^{32} - 14 q^{33} + 4 q^{34} - 12 q^{35} + 200 q^{36} - 2 q^{37} - 18 q^{38} - 10 q^{39} + 12 q^{40} - 18 q^{41} + 12 q^{42} - 28 q^{43} - 48 q^{44} - 16 q^{45} - 4 q^{46} + 2 q^{47} - 50 q^{48} + 239 q^{49} + 14 q^{50} - 24 q^{51} + 12 q^{52} - 8 q^{53} - 52 q^{54} - 8 q^{55} - 34 q^{56} - 12 q^{57} + 8 q^{58} - 10 q^{59} - 22 q^{60} + 6 q^{61} + 4 q^{63} + 174 q^{64} - 8 q^{65} - 16 q^{66} - 12 q^{67} - 22 q^{69} + 54 q^{70} - 20 q^{71} + 20 q^{72} - 4 q^{73} + 16 q^{74} - 62 q^{75} - 8 q^{76} - 44 q^{77} + 20 q^{78} - 22 q^{79} + 46 q^{80} + 259 q^{81} + 42 q^{82} + 16 q^{83} + 14 q^{84} + 10 q^{85} - 16 q^{87} - 6 q^{89} - 42 q^{90} - 74 q^{91} - 56 q^{92} - 48 q^{93} - 2 q^{94} + 18 q^{95} - 100 q^{96} - 10 q^{97} - 22 q^{98} - 94 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3019))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3019
3019.2.a.a 3019.a 1.a $2$ $24.107$ \(\Q(\sqrt{5}) \) None \(-4\) \(-2\) \(-2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}-2\beta q^{5}+2q^{6}+\cdots\)
3019.2.a.b 3019.a 1.a $119$ $24.107$ None \(-15\) \(-17\) \(-61\) \(-16\) $+$ $\mathrm{SU}(2)$
3019.2.a.c 3019.a 1.a $130$ $24.107$ None \(17\) \(15\) \(63\) \(16\) $-$ $\mathrm{SU}(2)$