Properties

Label 231.2.l
Level $231$
Weight $2$
Character orbit 231.l
Rep. character $\chi_{231}(32,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $56$
Newform subspaces $2$
Sturm bound $64$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 231.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(64\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(231, [\chi])\).

Total New Old
Modular forms 72 72 0
Cusp forms 56 56 0
Eisenstein series 16 16 0

Trace form

\( 56 q - 2 q^{3} - 28 q^{4} - 6 q^{9} + O(q^{10}) \) \( 56 q - 2 q^{3} - 28 q^{4} - 6 q^{9} + 6 q^{12} - 12 q^{15} - 44 q^{16} - 24 q^{22} - 12 q^{25} + 4 q^{27} - 22 q^{33} + 56 q^{34} + 28 q^{36} + 96 q^{42} + 14 q^{45} - 104 q^{48} - 4 q^{49} - 88 q^{55} + 16 q^{58} - 48 q^{60} + 192 q^{64} - 42 q^{66} + 20 q^{67} - 28 q^{69} - 76 q^{70} + 46 q^{75} + 104 q^{78} + 2 q^{81} - 4 q^{82} - 16 q^{88} + 48 q^{91} + 48 q^{93} - 80 q^{97} - 20 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(231, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
231.2.l.a 231.l 231.l $8$ $1.845$ 8.0.\(\cdots\).5 None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}+\beta _{4})q^{3}+2\beta _{4}q^{4}+(-\beta _{2}-\beta _{7})q^{5}+\cdots\)
231.2.l.b 231.l 231.l $48$ $1.845$ None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$