Properties

Label 288.1.t
Level $288$
Weight $1$
Character orbit 288.t
Rep. character $\chi_{288}(79,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 288.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(288, [\chi])\).

Total New Old
Modular forms 24 6 18
Cusp forms 8 2 6
Eisenstein series 16 4 12

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2 q + q^{3} - q^{9} + O(q^{10}) \) \( 2 q + q^{3} - q^{9} - q^{11} - 2 q^{17} + 2 q^{19} - q^{25} - 2 q^{27} + q^{33} + q^{41} - q^{43} - q^{49} - q^{51} + q^{57} - q^{59} - q^{67} - 2 q^{73} + q^{75} - q^{81} + 2 q^{83} + 4 q^{89} + q^{97} + 2 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(288, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
288.1.t.a \(2\) \(0.144\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-2}) \) None \(0\) \(1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+\zeta_{6}^{2}q^{11}-q^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(288, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(288, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)