Properties

Label 224.3.n
Level 224
Weight 3
Character orbit n
Rep. character \(\chi_{224}(17,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 28
Newform subspaces 1
Sturm bound 96
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(224, [\chi])\).

Total New Old
Modular forms 144 36 108
Cusp forms 112 28 84
Eisenstein series 32 8 24

Trace form

\( 28q + 4q^{7} - 32q^{9} + O(q^{10}) \) \( 28q + 4q^{7} - 32q^{9} - 28q^{15} - 6q^{17} - 30q^{23} - 32q^{25} + 6q^{31} - 6q^{33} + 20q^{39} + 294q^{47} - 20q^{49} + 124q^{57} - 432q^{63} - 52q^{65} + 136q^{71} + 234q^{73} + 162q^{79} - 18q^{81} - 48q^{87} - 150q^{89} - 290q^{95} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(224, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
224.3.n.a \(28\) \(6.104\) None \(0\) \(0\) \(0\) \(4\)

Decomposition of \(S_{3}^{\mathrm{old}}(224, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(224, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 3}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database