Properties

Label 224.2.bd
Level 224
Weight 2
Character orbit bd
Rep. character \(\chi_{224}(37,\cdot)\)
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.bd (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

\( 240q - 4q^{2} - 4q^{3} - 4q^{4} - 4q^{5} - 16q^{6} - 8q^{7} - 16q^{8} - 4q^{9} + O(q^{10}) \) \( 240q - 4q^{2} - 4q^{3} - 4q^{4} - 4q^{5} - 16q^{6} - 8q^{7} - 16q^{8} - 4q^{9} - 4q^{10} - 4q^{11} - 4q^{12} - 16q^{13} + 24q^{14} - 24q^{16} - 24q^{18} - 4q^{19} - 48q^{20} - 8q^{21} - 24q^{22} - 12q^{23} + 36q^{24} - 4q^{25} - 4q^{26} - 16q^{27} + 12q^{28} - 16q^{29} + 44q^{30} - 56q^{31} - 4q^{32} - 8q^{33} - 32q^{34} - 32q^{35} - 96q^{36} - 4q^{37} + 36q^{38} - 4q^{39} - 68q^{40} - 16q^{41} - 28q^{42} + 44q^{44} + 8q^{45} - 4q^{46} - 16q^{48} + 8q^{50} - 28q^{51} - 28q^{52} - 20q^{53} - 92q^{54} - 16q^{55} - 48q^{56} - 16q^{57} + 28q^{58} - 36q^{59} + 60q^{60} - 4q^{61} - 16q^{63} + 56q^{64} - 8q^{65} - 36q^{66} + 36q^{67} - 36q^{68} - 16q^{69} - 44q^{70} + 48q^{71} - 4q^{72} - 4q^{73} + 68q^{74} + 16q^{75} - 16q^{76} - 8q^{77} - 120q^{78} - 16q^{80} - 44q^{82} - 96q^{83} - 28q^{84} - 56q^{85} - 4q^{86} - 4q^{87} + 40q^{88} - 4q^{89} + 224q^{90} - 56q^{91} - 80q^{92} + 20q^{93} + 4q^{94} - 8q^{95} - 32q^{96} - 32q^{97} + 96q^{98} + 8q^{99} + O(q^{100}) \)

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.bd.a \(240\) \(1.789\) None \(-4\) \(-4\) \(-4\) \(-8\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database