Properties

Label 3023.2.a
Level 3023
Weight 2
Character orbit 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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3023
3023.2.a.a \(1\) \(24.139\) \(\Q\) None \(-1\) \(0\) \(2\) \(0\) \(+\) \(q-q^{2}-q^{4}+2q^{5}+3q^{8}-3q^{9}-2q^{10}+\cdots\)
3023.2.a.b \(102\) \(24.139\) None \(-11\) \(-16\) \(-17\) \(-53\) \(+\)
3023.2.a.c \(149\) \(24.139\) None \(13\) \(16\) \(15\) \(59\) \(-\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T + 2 T^{2} \))
$3$ (\( 1 + 3 T^{2} \))
$5$ (\( 1 - 2 T + 5 T^{2} \))
$7$ (\( 1 + 7 T^{2} \))
$11$ (\( 1 - 5 T + 11 T^{2} \))
$13$ (\( 1 + 4 T + 13 T^{2} \))
$17$ (\( 1 - 2 T + 17 T^{2} \))
$19$ (\( 1 + 2 T + 19 T^{2} \))
$23$ (\( 1 + 6 T + 23 T^{2} \))
$29$ (\( 1 + T + 29 T^{2} \))
$31$ (\( 1 - 5 T + 31 T^{2} \))
$37$ (\( 1 - 3 T + 37 T^{2} \))
$41$ (\( 1 - 2 T + 41 T^{2} \))
$43$ (\( 1 + 5 T + 43 T^{2} \))
$47$ (\( 1 + 10 T + 47 T^{2} \))
$53$ (\( 1 + 10 T + 53 T^{2} \))
$59$ (\( 1 + 59 T^{2} \))
$61$ (\( 1 - 15 T + 61 T^{2} \))
$67$ (\( 1 + 4 T + 67 T^{2} \))
$71$ (\( 1 - 4 T + 71 T^{2} \))
$73$ (\( 1 - 6 T + 73 T^{2} \))
$79$ (\( 1 + 3 T + 79 T^{2} \))
$83$ (\( 1 - 4 T + 83 T^{2} \))
$89$ (\( 1 + 6 T + 89 T^{2} \))
$97$ (\( 1 + 5 T + 97 T^{2} \))
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