Properties

Label 102.2.a
Level 102
Weight 2
Character orbit a
Rep. character \(\chi_{102}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newform subspaces 3
Sturm bound 36
Trace bound 3

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Defining parameters

Level: \( N \) \(=\) \( 102 = 2 \cdot 3 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 102.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(36\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(102))\).

Total New Old
Modular forms 22 3 19
Cusp forms 15 3 12
Eisenstein series 7 0 7

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

\(2\)\(3\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(2\)

Trace form

\( 3q - q^{2} + q^{3} + 3q^{4} - 6q^{5} + q^{6} - q^{8} + 3q^{9} + O(q^{10}) \) \( 3q - q^{2} + q^{3} + 3q^{4} - 6q^{5} + q^{6} - q^{8} + 3q^{9} + 2q^{10} - 4q^{11} + q^{12} - 6q^{13} + 2q^{15} + 3q^{16} - q^{17} - q^{18} + 4q^{19} - 6q^{20} + 4q^{21} - 4q^{22} + q^{24} + 5q^{25} + 2q^{26} + q^{27} - 14q^{29} - 6q^{30} - 8q^{31} - q^{32} - 4q^{33} + 3q^{34} + 8q^{35} + 3q^{36} + 2q^{37} + 4q^{38} + 6q^{39} + 2q^{40} + 6q^{41} - 4q^{42} + 4q^{43} - 4q^{44} - 6q^{45} + 16q^{47} + q^{48} - 13q^{49} - 7q^{50} + q^{51} - 6q^{52} + 10q^{53} + q^{54} + 8q^{55} - 4q^{57} - 6q^{58} + 12q^{59} + 2q^{60} - 6q^{61} + 24q^{62} + 3q^{64} + 28q^{65} - 4q^{66} - 28q^{67} - q^{68} - 12q^{69} - 8q^{70} - q^{72} + 14q^{73} - 6q^{74} - 17q^{75} + 4q^{76} - 10q^{78} - 8q^{79} - 6q^{80} + 3q^{81} + 14q^{82} + 4q^{83} + 4q^{84} + 2q^{85} + 20q^{86} - 6q^{87} - 4q^{88} - 26q^{89} + 2q^{90} + 16q^{91} + 4q^{93} - 16q^{94} - 24q^{95} + q^{96} + 6q^{97} - q^{98} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(102))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 17
102.2.a.a \(1\) \(0.814\) \(\Q\) None \(-1\) \(-1\) \(-4\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-2q^{7}+\cdots\)
102.2.a.b \(1\) \(0.814\) \(\Q\) None \(-1\) \(1\) \(0\) \(2\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
102.2.a.c \(1\) \(0.814\) \(\Q\) None \(1\) \(1\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(102))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(102)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 - T \))
$3$ (\( 1 + T \))(\( 1 - T \))(\( 1 - T \))
$5$ (\( 1 + 4 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))
$7$ (\( 1 + 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))
$11$ (\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))
$13$ (\( 1 + 6 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))
$17$ (\( 1 + T \))(\( 1 + T \))(\( 1 - T \))
$19$ (\( 1 - 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))
$23$ (\( 1 - 6 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))
$29$ (\( 1 + 4 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))
$31$ (\( 1 + 6 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))
$37$ (\( 1 + 4 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))
$41$ (\( 1 + 10 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))
$43$ (\( 1 + 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 12 T + 43 T^{2} \))
$47$ (\( 1 - 4 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))
$53$ (\( 1 + 2 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))
$59$ (\( 1 - 12 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))
$61$ (\( 1 + 4 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))
$67$ (\( 1 + 12 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))
$71$ (\( 1 + 6 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))
$73$ (\( 1 - 2 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))
$79$ (\( 1 - 10 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))
$83$ (\( 1 + 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))
$89$ (\( 1 + 2 T + 89 T^{2} \))(\( 1 + 18 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))
$97$ (\( 1 - 6 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))
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