Properties

Label 132.4.a
Level $132$
Weight $4$
Character orbit 132.a
Rep. character $\chi_{132}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $4$
Sturm bound $96$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 132.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(132))\).

Total New Old
Modular forms 78 4 74
Cusp forms 66 4 62
Eisenstein series 12 0 12

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
\(-\)\(+\)\(+\)$-$\(1\)
\(-\)\(+\)\(-\)$+$\(2\)
\(-\)\(-\)\(+\)$+$\(1\)
Plus space\(+\)\(3\)
Minus space\(-\)\(1\)

Trace form

\( 4 q - 6 q^{3} + 20 q^{5} + 4 q^{7} + 36 q^{9} + O(q^{10}) \) \( 4 q - 6 q^{3} + 20 q^{5} + 4 q^{7} + 36 q^{9} + 8 q^{13} + 132 q^{17} + 164 q^{19} + 36 q^{21} + 92 q^{23} + 228 q^{25} - 54 q^{27} + 188 q^{29} + 32 q^{31} - 66 q^{33} - 528 q^{35} - 64 q^{37} + 84 q^{39} + 244 q^{41} - 564 q^{43} + 180 q^{45} + 188 q^{47} - 708 q^{49} - 120 q^{51} - 708 q^{53} - 252 q^{57} - 216 q^{59} + 960 q^{61} + 36 q^{63} - 8 q^{65} - 520 q^{67} - 12 q^{69} - 1820 q^{71} + 16 q^{73} - 834 q^{75} - 176 q^{77} - 3068 q^{79} + 324 q^{81} + 1168 q^{83} + 2376 q^{85} + 552 q^{87} + 2152 q^{89} + 312 q^{91} - 528 q^{93} + 64 q^{95} + 384 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(132))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 11
132.4.a.a 132.a 1.a $1$ $7.788$ \(\Q\) None \(0\) \(-3\) \(-12\) \(14\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-12q^{5}+14q^{7}+9q^{9}+11q^{11}+\cdots\)
132.4.a.b 132.a 1.a $1$ $7.788$ \(\Q\) None \(0\) \(-3\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+2q^{7}+9q^{9}-11q^{11}-88q^{13}+\cdots\)
132.4.a.c 132.a 1.a $1$ $7.788$ \(\Q\) None \(0\) \(-3\) \(22\) \(-20\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+22q^{5}-20q^{7}+9q^{9}+11q^{11}+\cdots\)
132.4.a.d 132.a 1.a $1$ $7.788$ \(\Q\) None \(0\) \(3\) \(10\) \(8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+10q^{5}+8q^{7}+9q^{9}-11q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(132))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(132)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 2}\)