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Properties

Label 3022.2.a
Level $3022$
Weight $2$
Character orbit 3022.a
Rep. character $\chi_{3022}(1,\cdot)$
Character field $\Q$
Dimension $125$
Newform subspaces $4$
Sturm bound $756$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 3022 = 2 \cdot 1511 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3022.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(756\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3022))\).

Total New Old
Modular forms 380 125 255
Cusp forms 377 125 252
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(1511\)FrickeDim
\(+\)\(+\)$+$\(28\)
\(+\)\(-\)$-$\(35\)
\(-\)\(+\)$-$\(34\)
\(-\)\(-\)$+$\(28\)
Plus space\(+\)\(56\)
Minus space\(-\)\(69\)

Trace form

\( 125 q - q^{2} + 125 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} + 117 q^{9} + O(q^{10}) \) \( 125 q - q^{2} + 125 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} + 117 q^{9} - 6 q^{10} - 6 q^{11} - 10 q^{13} - 8 q^{14} - 4 q^{15} + 125 q^{16} + 2 q^{17} - 13 q^{18} - 16 q^{19} - 2 q^{20} - 8 q^{21} - 10 q^{22} + 4 q^{23} - 4 q^{24} + 107 q^{25} - 10 q^{26} + 12 q^{27} - 8 q^{28} - 12 q^{30} + 4 q^{31} - q^{32} + 4 q^{33} - 10 q^{34} - 16 q^{35} + 117 q^{36} + 8 q^{37} - 44 q^{39} - 6 q^{40} + 6 q^{41} - 8 q^{42} - 34 q^{43} - 6 q^{44} - 18 q^{45} - 16 q^{46} + 8 q^{47} + 93 q^{49} - 7 q^{50} - 36 q^{51} - 10 q^{52} - 16 q^{54} - 12 q^{55} - 8 q^{56} + 4 q^{57} - 16 q^{58} - 2 q^{59} - 4 q^{60} - 30 q^{61} - 4 q^{62} - 36 q^{63} + 125 q^{64} + 4 q^{65} - 24 q^{66} + 10 q^{67} + 2 q^{68} - 4 q^{69} - 16 q^{70} + 36 q^{71} - 13 q^{72} + 2 q^{73} - 16 q^{74} + 44 q^{75} - 16 q^{76} + 28 q^{77} + 20 q^{78} - 52 q^{79} - 2 q^{80} + 101 q^{81} + 2 q^{82} + 26 q^{83} - 8 q^{84} - 12 q^{85} - 2 q^{86} - 12 q^{87} - 10 q^{88} - 10 q^{89} - 22 q^{90} - 24 q^{91} + 4 q^{92} + 12 q^{93} - 20 q^{94} + 44 q^{95} - 4 q^{96} - 10 q^{97} - 17 q^{98} - 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3022))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 1511
3022.2.a.a 3022.a 1.a $28$ $24.131$ None \(-28\) \(-3\) \(-10\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$
3022.2.a.b 3022.a 1.a $28$ $24.131$ None \(28\) \(-9\) \(-16\) \(-23\) $-$ $-$ $\mathrm{SU}(2)$
3022.2.a.c 3022.a 1.a $34$ $24.131$ None \(34\) \(7\) \(12\) \(15\) $-$ $+$ $\mathrm{SU}(2)$
3022.2.a.d 3022.a 1.a $35$ $24.131$ None \(-35\) \(5\) \(12\) \(1\) $+$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3022))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3022)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(1511))\)\(^{\oplus 2}\)