Properties

Label 224.2.be
Level 224
Weight 2
Character orbit be
Rep. character \(\chi_{224}(3,\cdot)\)
Character field \(\Q(\zeta_{24})\)
Dimension 240
Newform subspaces 1
Sturm bound 64
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 224.be (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 224 \)
Character field: \(\Q(\zeta_{24})\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(224, [\chi])\).

Total New Old
Modular forms 272 272 0
Cusp forms 240 240 0
Eisenstein series 32 32 0

Trace form

\( 240q - 4q^{2} - 12q^{3} - 4q^{4} - 12q^{5} - 8q^{7} - 16q^{8} - 4q^{9} + O(q^{10}) \) \( 240q - 4q^{2} - 12q^{3} - 4q^{4} - 12q^{5} - 8q^{7} - 16q^{8} - 4q^{9} - 12q^{10} - 4q^{11} - 12q^{12} - 40q^{14} - 32q^{15} - 24q^{16} + 16q^{18} - 12q^{19} - 8q^{21} - 8q^{22} + 4q^{23} - 12q^{24} - 4q^{25} - 12q^{26} + 12q^{28} - 16q^{29} - 52q^{30} - 4q^{32} - 24q^{33} - 32q^{35} + 64q^{36} - 4q^{37} - 12q^{38} - 4q^{39} - 12q^{40} - 28q^{42} - 32q^{43} - 52q^{44} - 48q^{45} - 4q^{46} - 24q^{47} - 40q^{50} + 20q^{51} + 60q^{52} - 20q^{53} - 12q^{54} - 48q^{56} - 16q^{57} - 36q^{58} + 84q^{59} + 28q^{60} - 12q^{61} - 136q^{64} - 8q^{65} + 132q^{66} + 36q^{67} - 12q^{68} + 28q^{70} - 80q^{71} - 4q^{72} - 12q^{73} - 20q^{74} - 72q^{75} - 8q^{77} - 216q^{78} - 8q^{79} + 24q^{80} + 108q^{82} + 12q^{84} + 24q^{85} - 4q^{86} - 12q^{87} - 48q^{88} - 12q^{89} + 40q^{91} - 80q^{92} + 20q^{93} + 60q^{94} + 312q^{96} - 16q^{98} - 40q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(224, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
224.2.be.a \(240\) \(1.789\) None \(-4\) \(-12\) \(-12\) \(-8\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database