Properties

Label 432.2.y
Level $432$
Weight $2$
Character orbit 432.y
Rep. character $\chi_{432}(37,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $88$
Newform subspaces $5$
Sturm bound $144$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.y (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 5 \)
Sturm bound: \(144\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 312 104 208
Cusp forms 264 88 176
Eisenstein series 48 16 32

Trace form

\( 88q + 2q^{2} - 2q^{4} + 2q^{5} + 8q^{8} + O(q^{10}) \) \( 88q + 2q^{2} - 2q^{4} + 2q^{5} + 8q^{8} - 8q^{10} + 2q^{11} - 2q^{13} + 10q^{14} - 2q^{16} + 16q^{17} - 8q^{19} - 12q^{20} - 2q^{22} + 40q^{26} - 24q^{28} + 2q^{29} - 4q^{31} + 22q^{32} - 6q^{34} + 28q^{35} - 8q^{37} - 26q^{38} - 2q^{40} - 2q^{43} - 36q^{44} + 8q^{46} + 44q^{47} + 16q^{49} + 36q^{50} - 2q^{52} + 8q^{53} - 52q^{56} - 20q^{58} - 10q^{59} - 2q^{61} - 100q^{62} - 44q^{64} + 4q^{65} - 2q^{67} - 16q^{68} + 12q^{70} - 26q^{74} + 10q^{76} + 30q^{77} - 4q^{79} - 144q^{80} - 52q^{82} + 22q^{83} - 12q^{85} - 70q^{86} - 26q^{88} - 36q^{91} + 56q^{92} + 6q^{94} - 60q^{95} - 4q^{97} - 40q^{98} + O(q^{100}) \)

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.y.a \(4\) \(3.450\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(-2\) \(-12\) \(q+(-1-\zeta_{12}+\zeta_{12}^{2})q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{4}+\cdots\)
432.2.y.b \(4\) \(3.450\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(-4\) \(6\) \(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots\)
432.2.y.c \(4\) \(3.450\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(8\) \(-6\) \(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots\)
432.2.y.d \(4\) \(3.450\) \(\Q(\zeta_{12})\) None \(4\) \(0\) \(4\) \(12\) \(q+(1+\zeta_{12}^{3})q^{2}+2\zeta_{12}^{3}q^{4}+(1+\zeta_{12}+\cdots)q^{5}+\cdots\)
432.2.y.e \(72\) \(3.450\) None \(-4\) \(0\) \(-4\) \(0\)

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

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