Properties

Label 432.2.s
Level $432$
Weight $2$
Character orbit 432.s
Rep. character $\chi_{432}(143,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $5$
Sturm bound $144$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(144\)
Trace bound: \(7\)
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 180 12 168
Cusp forms 108 12 96
Eisenstein series 72 0 72

Trace form

\( 12q + O(q^{10}) \) \( 12q + 6q^{25} + 36q^{29} + 18q^{41} + 6q^{49} - 72q^{65} - 36q^{73} - 72q^{77} - 18q^{97} + O(q^{100}) \)

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.s.a \(2\) \(3.450\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(-3\) \(q+(-2+\zeta_{6})q^{5}+(-1-\zeta_{6})q^{7}+(-3+\cdots)q^{11}+\cdots\)
432.2.s.b \(2\) \(3.450\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(3\) \(q+(-2+\zeta_{6})q^{5}+(1+\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
432.2.s.c \(2\) \(3.450\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(6\) \(-6\) \(q+(4-2\zeta_{6})q^{5}+(-2-2\zeta_{6})q^{7}+(3+\cdots)q^{11}+\cdots\)
432.2.s.d \(2\) \(3.450\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(6\) \(6\) \(q+(4-2\zeta_{6})q^{5}+(2+2\zeta_{6})q^{7}+(-3+\cdots)q^{11}+\cdots\)
432.2.s.e \(4\) \(3.450\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-6\) \(0\) \(q+(-2+\zeta_{12}^{2})q^{5}+\zeta_{12}q^{7}+(-\zeta_{12}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(432, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)