Properties

Label 672.2.cl
Level 672
Weight 2
Character orbit cl
Rep. character \(\chi_{672}(5,\cdot)\)
Character field \(\Q(\zeta_{24})\)
Dimension 992
Newform subspaces 1
Sturm bound 256
Trace bound 0

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Defining parameters

Level: \( N \) = \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 672.cl (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 672 \)
Character field: \(\Q(\zeta_{24})\)
Newform subspaces: \( 1 \)
Sturm bound: \(256\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(672, [\chi])\).

Total New Old
Modular forms 1056 1056 0
Cusp forms 992 992 0
Eisenstein series 64 64 0

Trace form

\( 992q - 12q^{3} - 8q^{4} - 16q^{7} - 4q^{9} + O(q^{10}) \) \( 992q - 12q^{3} - 8q^{4} - 16q^{7} - 4q^{9} - 24q^{10} - 12q^{12} + 24q^{16} - 4q^{18} - 24q^{19} - 8q^{21} - 32q^{22} - 12q^{24} - 8q^{25} - 16q^{28} + 28q^{30} - 48q^{31} - 24q^{33} - 96q^{36} - 8q^{37} - 4q^{39} - 24q^{40} - 68q^{42} - 32q^{43} - 12q^{45} - 8q^{46} - 28q^{51} - 96q^{52} - 12q^{54} - 16q^{57} - 40q^{58} + 12q^{60} - 24q^{61} - 16q^{63} + 64q^{64} - 12q^{66} - 72q^{67} - 16q^{70} - 4q^{72} - 24q^{73} - 72q^{75} + 136q^{78} + 96q^{82} - 140q^{84} - 112q^{85} - 12q^{87} - 8q^{88} + 32q^{91} - 28q^{93} - 96q^{94} + 192q^{96} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(672, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
672.2.cl.a \(992\) \(5.366\) None \(0\) \(-12\) \(0\) \(-16\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database