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

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

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 11
132.2.a.a 132.a 1.a $1$ $1.054$ \(\Q\) None 132.2.a.a \(0\) \(-1\) \(2\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+2q^{7}+q^{9}-q^{11}+6q^{13}+\cdots\)
132.2.a.b 132.a 1.a $1$ $1.054$ \(\Q\) None 132.2.a.b \(0\) \(1\) \(2\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-2q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)

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

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