Properties

Label 432.2.v
Level 432
Weight 2
Character orbit v
Rep. character \(\chi_{432}(35,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 88
Newform subspaces 1
Sturm bound 144
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 432.v (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

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

\( 88q + 6q^{2} - 2q^{4} + 6q^{5} - 4q^{7} + O(q^{10}) \) \( 88q + 6q^{2} - 2q^{4} + 6q^{5} - 4q^{7} - 8q^{10} + 6q^{11} - 2q^{13} + 6q^{14} - 2q^{16} - 8q^{19} + 48q^{20} - 2q^{22} + 12q^{23} + 8q^{28} + 6q^{29} + 6q^{32} + 2q^{34} - 8q^{37} + 6q^{38} - 2q^{40} - 2q^{43} - 40q^{46} - 24q^{49} - 72q^{50} - 2q^{52} - 16q^{55} - 36q^{56} + 16q^{58} + 42q^{59} - 2q^{61} - 44q^{64} + 12q^{65} - 2q^{67} - 96q^{68} - 16q^{70} - 78q^{74} - 14q^{76} + 6q^{77} - 36q^{82} - 54q^{83} + 8q^{85} - 54q^{86} + 22q^{88} + 20q^{91} - 108q^{92} + 6q^{94} - 4q^{97} + O(q^{100}) \)

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.v.a \(88\) \(3.450\) None \(6\) \(0\) \(6\) \(-4\)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database