Properties

Label 106.2.a
Level 106
Weight 2
Character orbit a
Rep. character \(\chi_{106}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 4
Sturm bound 27
Trace bound 3

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Defining parameters

Level: \( N \) \(=\) \( 106 = 2 \cdot 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 106.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(27\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(106))\).

Total New Old
Modular forms 15 4 11
Cusp forms 12 4 8
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.

\(2\)\(53\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(2\)
Plus space\(+\)\(1\)
Minus space\(-\)\(3\)

Trace form

\( 4q + 4q^{4} - 2q^{6} - 4q^{7} - 2q^{9} + O(q^{10}) \) \( 4q + 4q^{4} - 2q^{6} - 4q^{7} - 2q^{9} + 6q^{10} - 2q^{11} - 2q^{13} + 4q^{16} + 8q^{17} - 16q^{19} - 12q^{21} - 4q^{22} - 8q^{23} - 2q^{24} + 6q^{25} + 4q^{26} - 4q^{28} + 14q^{29} - 12q^{30} + 4q^{31} + 20q^{33} - 8q^{34} + 4q^{35} - 2q^{36} - 10q^{37} + 6q^{38} + 4q^{39} + 6q^{40} + 4q^{41} - 4q^{42} - 14q^{43} - 2q^{44} + 12q^{45} - 4q^{46} + 4q^{47} - 4q^{49} - 8q^{50} - 8q^{51} - 2q^{52} - 2q^{53} - 2q^{54} + 12q^{55} + 6q^{57} + 16q^{58} + 22q^{59} + 4q^{61} - 2q^{62} + 8q^{63} + 4q^{64} - 20q^{65} - 8q^{66} + 12q^{67} + 8q^{68} + 14q^{69} + 8q^{70} + 36q^{71} - 16q^{73} - 32q^{75} - 16q^{76} - 16q^{77} + 22q^{78} - 8q^{79} - 20q^{81} + 20q^{82} - 20q^{83} - 12q^{84} - 8q^{85} - 8q^{86} - 20q^{87} - 4q^{88} + 46q^{89} - 6q^{90} - 20q^{91} - 8q^{92} + 4q^{93} + 8q^{94} + 12q^{95} - 2q^{96} + 16q^{98} + 10q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(106))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 53
106.2.a.a \(1\) \(0.846\) \(\Q\) None \(-1\) \(-1\) \(-4\) \(0\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-q^{8}+\cdots\)
106.2.a.b \(1\) \(0.846\) \(\Q\) None \(-1\) \(2\) \(1\) \(-2\) \(+\) \(-\) \(q-q^{2}+2q^{3}+q^{4}+q^{5}-2q^{6}-2q^{7}+\cdots\)
106.2.a.c \(1\) \(0.846\) \(\Q\) None \(1\) \(-2\) \(3\) \(2\) \(-\) \(+\) \(q+q^{2}-2q^{3}+q^{4}+3q^{5}-2q^{6}+2q^{7}+\cdots\)
106.2.a.d \(1\) \(0.846\) \(\Q\) None \(1\) \(1\) \(0\) \(-4\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(106))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(106)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(53))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))
$3$ (\( 1 + T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))
$5$ (\( 1 + 4 T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))
$7$ (\( 1 + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))
$11$ (\( 1 + 4 T + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))
$13$ (\( 1 - T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))
$17$ (\( 1 - 5 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))
$19$ (\( 1 + 7 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))
$23$ (\( 1 - T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))
$29$ (\( 1 - 5 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))
$31$ (\( 1 + 4 T + 31 T^{2} \))(\( 1 - 7 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))
$37$ (\( 1 - T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 5 T + 37 T^{2} \))
$41$ (\( 1 + 10 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))
$43$ (\( 1 + 10 T + 43 T^{2} \))(\( 1 - 7 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))
$47$ (\( 1 + 6 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))
$53$ (\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))
$59$ (\( 1 + 6 T + 59 T^{2} \))(\( 1 - 7 T + 59 T^{2} \))(\( 1 - 15 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))
$61$ (\( 1 - 4 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))
$67$ (\( 1 - 4 T + 67 T^{2} \))(\( 1 - 16 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))
$71$ (\( 1 - 15 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 3 T + 71 T^{2} \))
$73$ (\( 1 + 8 T + 73 T^{2} \))(\( 1 + 12 T + 73 T^{2} \))(\( 1 - 8 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))
$79$ (\( 1 - T + 79 T^{2} \))(\( 1 + 7 T + 79 T^{2} \))(\( 1 - 11 T + 79 T^{2} \))(\( 1 + 13 T + 79 T^{2} \))
$83$ (\( 1 + 3 T + 83 T^{2} \))(\( 1 + 14 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 3 T + 83 T^{2} \))
$89$ (\( 1 - 2 T + 89 T^{2} \))(\( 1 - 17 T + 89 T^{2} \))(\( 1 - 9 T + 89 T^{2} \))(\( 1 - 18 T + 89 T^{2} \))
$97$ (\( 1 - 17 T + 97 T^{2} \))(\( 1 - 3 T + 97 T^{2} \))(\( 1 + 13 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))
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