Properties

Label 118.2.a
Level 118
Weight 2
Character orbit a
Rep. character \(\chi_{118}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 4
Sturm bound 30
Trace bound 3

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Defining parameters

Level: \( N \) \(=\) \( 118 = 2 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 118.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(30\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(118))\).

Total New Old
Modular forms 17 4 13
Cusp forms 14 4 10
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.

\(2\)\(59\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(2\)
Plus space\(+\)\(1\)
Minus space\(-\)\(3\)

Trace form

\( 4q + 2q^{3} + 4q^{4} - 2q^{5} - 4q^{7} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{3} + 4q^{4} - 2q^{5} - 4q^{7} - 2q^{9} + 2q^{12} - 8q^{13} + 4q^{14} + 2q^{15} + 4q^{16} + 2q^{17} - 6q^{19} - 2q^{20} - 14q^{21} + 2q^{22} + 16q^{23} - 2q^{25} - 10q^{26} + 2q^{27} - 4q^{28} - 6q^{29} - 12q^{30} + 4q^{31} + 8q^{34} + 6q^{35} - 2q^{36} - 12q^{37} + 4q^{38} + 8q^{39} + 8q^{41} - 4q^{42} - 12q^{43} + 4q^{45} + 4q^{47} + 2q^{48} - 8q^{50} + 16q^{51} - 8q^{52} + 10q^{53} + 12q^{55} + 4q^{56} - 6q^{57} + 4q^{58} - 2q^{59} + 2q^{60} - 12q^{61} - 8q^{62} - 10q^{63} + 4q^{64} + 12q^{65} - 8q^{66} + 16q^{67} + 2q^{68} + 20q^{69} + 12q^{70} + 10q^{71} + 12q^{73} + 14q^{74} - 4q^{75} - 6q^{76} + 8q^{77} - 8q^{78} + 12q^{79} - 2q^{80} - 20q^{81} - 16q^{82} - 24q^{83} - 14q^{84} - 12q^{85} + 18q^{86} + 6q^{87} + 2q^{88} + 16q^{89} - 12q^{90} - 16q^{91} + 16q^{92} - 28q^{93} + 12q^{94} - 38q^{95} + 24q^{97} + 8q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(118))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 59
118.2.a.a \(1\) \(0.942\) \(\Q\) None \(-1\) \(-1\) \(-3\) \(-1\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
118.2.a.b \(1\) \(0.942\) \(\Q\) None \(-1\) \(2\) \(2\) \(-3\) \(+\) \(-\) \(q-q^{2}+2q^{3}+q^{4}+2q^{5}-2q^{6}-3q^{7}+\cdots\)
118.2.a.c \(1\) \(0.942\) \(\Q\) None \(1\) \(-1\) \(1\) \(3\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots\)
118.2.a.d \(1\) \(0.942\) \(\Q\) None \(1\) \(2\) \(-2\) \(-3\) \(-\) \(+\) \(q+q^{2}+2q^{3}+q^{4}-2q^{5}+2q^{6}-3q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(118))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(118)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))
$3$ (\( 1 + T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))
$5$ (\( 1 + 3 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))
$7$ (\( 1 + T + 7 T^{2} \))(\( 1 + 3 T + 7 T^{2} \))(\( 1 - 3 T + 7 T^{2} \))(\( 1 + 3 T + 7 T^{2} \))
$11$ (\( 1 + 2 T + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 + T + 11 T^{2} \))
$13$ (\( 1 + 2 T + 13 T^{2} \))(\( 1 - 3 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 + 3 T + 13 T^{2} \))
$17$ (\( 1 + 2 T + 17 T^{2} \))(\( 1 + T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 7 T + 17 T^{2} \))
$19$ (\( 1 - 3 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))
$23$ (\( 1 + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))
$29$ (\( 1 + T + 29 T^{2} \))(\( 1 + 4 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 - 4 T + 29 T^{2} \))
$31$ (\( 1 - 10 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))
$37$ (\( 1 + 12 T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))
$41$ (\( 1 - 7 T + 41 T^{2} \))(\( 1 - 5 T + 41 T^{2} \))(\( 1 - 7 T + 41 T^{2} \))(\( 1 + 11 T + 41 T^{2} \))
$43$ (\( 1 + 6 T + 43 T^{2} \))(\( 1 + 9 T + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( 1 - 9 T + 43 T^{2} \))
$47$ (\( 1 + 6 T + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 - 10 T + 47 T^{2} \))
$53$ (\( 1 + 11 T + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))(\( 1 - 9 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))
$59$ (\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))
$61$ (\( 1 + 12 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))
$67$ (\( 1 - 10 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))
$71$ (\( 1 - 4 T + 71 T^{2} \))(\( 1 + 15 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 9 T + 71 T^{2} \))
$73$ (\( 1 - 12 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))
$79$ (\( 1 + 15 T + 79 T^{2} \))(\( 1 - 11 T + 79 T^{2} \))(\( 1 - 5 T + 79 T^{2} \))(\( 1 - 11 T + 79 T^{2} \))
$83$ (\( 1 + 14 T + 83 T^{2} \))(\( 1 + 11 T + 83 T^{2} \))(\( 1 - 14 T + 83 T^{2} \))(\( 1 + 13 T + 83 T^{2} \))
$89$ (\( 1 - 4 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 - 18 T + 89 T^{2} \))
$97$ (\( 1 + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))
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