Properties

Label 132.2.h
Level $132$
Weight $2$
Character orbit 132.h
Rep. character $\chi_{132}(43,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 132.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 44 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(132, [\chi])\).

Total New Old
Modular forms 28 12 16
Cusp forms 20 12 8
Eisenstein series 8 0 8

Trace form

\( 12 q + 4 q^{4} - 12 q^{9} + O(q^{10}) \) \( 12 q + 4 q^{4} - 12 q^{9} - 8 q^{12} + 4 q^{14} + 4 q^{16} - 28 q^{20} - 4 q^{22} + 20 q^{25} - 12 q^{26} + 4 q^{33} + 40 q^{34} - 4 q^{36} - 32 q^{37} - 8 q^{38} - 12 q^{42} + 36 q^{44} + 16 q^{48} - 12 q^{49} - 16 q^{53} - 20 q^{56} + 24 q^{58} + 12 q^{60} - 20 q^{64} + 8 q^{66} - 64 q^{70} + 48 q^{77} + 20 q^{78} + 52 q^{80} + 12 q^{81} - 32 q^{82} + 72 q^{86} + 12 q^{88} - 8 q^{89} - 12 q^{92} + 16 q^{93} - 48 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(132, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
132.2.h.a 132.h 44.c $12$ $1.054$ 12.0.\(\cdots\).2 None 132.2.h.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(\beta _{2}+\beta _{3})q^{4}+(\beta _{6}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(132, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(132, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 2}\)