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Properties

Label 3023.2.a
Level $3023$
Weight $2$
Character orbit 3023.a
Rep. character $\chi_{3023}(1,\cdot)$
Character field $\Q$
Dimension $252$
Newform subspaces $3$
Sturm bound $504$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 3023 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3023.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(504\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3023))\).

Total New Old
Modular forms 253 253 0
Cusp forms 252 252 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.

\(3023\)Dim
\(+\)\(103\)
\(-\)\(149\)

Trace form

\( 252 q + q^{2} + 251 q^{4} - 2 q^{6} + 6 q^{7} + 3 q^{8} + 250 q^{9} + O(q^{10}) \) \( 252 q + q^{2} + 251 q^{4} - 2 q^{6} + 6 q^{7} + 3 q^{8} + 250 q^{9} - 8 q^{10} - 4 q^{11} + 4 q^{13} - 6 q^{15} + 253 q^{16} + 6 q^{17} + 19 q^{18} + 2 q^{19} - 2 q^{20} - 4 q^{21} + 6 q^{22} + 10 q^{23} + 262 q^{25} - 22 q^{26} + 26 q^{28} - 6 q^{29} - 14 q^{30} - 12 q^{31} - 3 q^{32} + 12 q^{33} + 8 q^{34} - 16 q^{35} + 229 q^{36} + 18 q^{37} + 22 q^{38} + 6 q^{39} - 30 q^{40} + 10 q^{41} - 12 q^{42} + 2 q^{43} + 8 q^{44} - 2 q^{45} - 8 q^{46} + 8 q^{47} + 30 q^{48} + 260 q^{49} - 9 q^{50} + 12 q^{51} + 26 q^{52} - 6 q^{53} + 10 q^{54} - 4 q^{55} + 20 q^{56} + 30 q^{57} + 34 q^{58} + 22 q^{59} - 66 q^{60} + 4 q^{61} - 12 q^{62} + 66 q^{63} + 259 q^{64} + 42 q^{65} + 10 q^{66} + 2 q^{67} + 18 q^{68} - 32 q^{69} + 8 q^{71} + 15 q^{72} + 54 q^{73} + 32 q^{74} + 18 q^{75} - 28 q^{76} - 14 q^{77} - 40 q^{78} - 2 q^{79} - 46 q^{80} + 236 q^{81} - 44 q^{82} + 18 q^{83} - 4 q^{84} + 52 q^{85} - 30 q^{86} + 20 q^{87} + 20 q^{88} - 24 q^{89} - 146 q^{90} + 20 q^{91} - 16 q^{92} + 6 q^{93} - 16 q^{94} - 34 q^{95} - 68 q^{96} + 34 q^{97} - 69 q^{98} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3023))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3023
3023.2.a.a 3023.a 1.a $1$ $24.139$ \(\Q\) None \(-1\) \(0\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+2q^{5}+3q^{8}-3q^{9}-2q^{10}+\cdots\)
3023.2.a.b 3023.a 1.a $102$ $24.139$ None \(-11\) \(-16\) \(-17\) \(-53\) $+$ $\mathrm{SU}(2)$
3023.2.a.c 3023.a 1.a $149$ $24.139$ None \(13\) \(16\) \(15\) \(59\) $-$ $\mathrm{SU}(2)$