↑

Properties

Label 132.2.p
Level $132$
Weight $2$
Character orbit 132.p
Rep. character $\chi_{132}(17,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $16$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 132.p (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
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 120 16 104
Cusp forms 72 16 56
Eisenstein series 48 0 48

Trace form

\( 16 q + q^{3} + 5 q^{9} + O(q^{10}) \) \( 16 q + q^{3} + 5 q^{9} + 9 q^{15} - 30 q^{19} - 12 q^{25} + q^{27} - 10 q^{31} - 41 q^{33} - 24 q^{37} - 35 q^{39} + 2 q^{45} + 12 q^{49} - 15 q^{51} + 62 q^{55} + 35 q^{57} + 40 q^{61} + 55 q^{63} + 44 q^{67} + 46 q^{69} + 10 q^{73} + 21 q^{75} + 20 q^{79} + 57 q^{81} - 60 q^{85} - 60 q^{91} + 7 q^{93} - 36 q^{97} - 101 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
132.2.p.a 132.p 33.f $16$ $1.054$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q-\beta _{12}q^{3}-\beta _{15}q^{5}+(1-\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(132, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 2}\)