Properties

Label 231.2.c
Level $231$
Weight $2$
Character orbit 231.c
Rep. character $\chi_{231}(76,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 231.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 36 16 20
Cusp forms 28 16 12
Eisenstein series 8 0 8

Trace form

\( 16 q - 12 q^{4} - 16 q^{9} + O(q^{10}) \) \( 16 q - 12 q^{4} - 16 q^{9} + 16 q^{11} + 8 q^{14} - 8 q^{15} - 4 q^{16} - 20 q^{22} + 24 q^{23} - 24 q^{25} + 12 q^{36} + 8 q^{37} + 12 q^{42} - 32 q^{44} + 24 q^{53} - 40 q^{56} - 12 q^{58} + 36 q^{60} + 88 q^{64} - 32 q^{67} + 36 q^{70} - 48 q^{71} + 12 q^{78} + 16 q^{81} + 32 q^{86} + 16 q^{91} - 128 q^{92} - 40 q^{93} - 16 q^{99} + O(q^{100}) \)

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.c.a 231.c 77.b $16$ $1.845$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{2}-\beta _{8}q^{3}+(-1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(231, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(231, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)