Properties

Label 132.2.a
Level $132$
Weight $2$
Character orbit 132.a
Rep. character $\chi_{132}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $48$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 132.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(132))\).

Total New Old
Modular forms 30 2 28
Cusp forms 19 2 17
Eisenstein series 11 0 11

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

\(2\)\(3\)\(11\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(2\)

Trace form

\( 2q + 4q^{5} + 2q^{9} + O(q^{10}) \) \( 2q + 4q^{5} + 2q^{9} + 4q^{13} - 8q^{19} - 4q^{21} - 8q^{23} - 2q^{25} - 8q^{29} - 8q^{31} + 2q^{33} + 4q^{37} - 8q^{39} + 8q^{41} + 8q^{43} + 4q^{45} - 8q^{47} - 6q^{49} + 8q^{51} + 12q^{53} - 4q^{57} - 4q^{61} + 8q^{65} + 16q^{67} + 8q^{69} + 8q^{71} + 12q^{73} - 4q^{77} + 2q^{81} + 32q^{83} - 8q^{87} - 28q^{89} + 16q^{91} - 8q^{93} - 16q^{95} - 4q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(132))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 11
132.2.a.a \(1\) \(1.054\) \(\Q\) None \(0\) \(-1\) \(2\) \(2\) \(-\) \(+\) \(+\) \(q-q^{3}+2q^{5}+2q^{7}+q^{9}-q^{11}+6q^{13}+\cdots\)
132.2.a.b \(1\) \(1.054\) \(\Q\) None \(0\) \(1\) \(2\) \(-2\) \(-\) \(-\) \(-\) \(q+q^{3}+2q^{5}-2q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(132))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(132)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

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