Properties

Label 432.2.be
Level $432$
Weight $2$
Character orbit 432.be
Rep. character $\chi_{432}(47,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $108$
Newform subspaces $3$
Sturm bound $144$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.be (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 108 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 3 \)
Sturm bound: \(144\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(432, [\chi])\).

Total New Old
Modular forms 468 108 360
Cusp forms 396 108 288
Eisenstein series 72 0 72

Trace form

\( 108 q + O(q^{10}) \) \( 108 q + 36 q^{29} + 18 q^{33} + 18 q^{41} + 36 q^{45} - 18 q^{57} - 72 q^{65} - 72 q^{69} - 72 q^{77} - 72 q^{81} - 54 q^{89} - 72 q^{93} + 54 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(432, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
432.2.be.a $36$ $3.450$ None \(0\) \(0\) \(-6\) \(0\)
432.2.be.b $36$ $3.450$ None \(0\) \(0\) \(3\) \(0\)
432.2.be.c $36$ $3.450$ None \(0\) \(0\) \(3\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(432, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 3}\)