Properties

Label 672.2.ch
Level 672
Weight 2
Character orbit ch
Rep. character \(\chi_{672}(11,\cdot)\)
Character field \(\Q(\zeta_{24})\)
Dimension 992
Newform subspaces 1
Sturm bound 256
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 672.ch (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

\( 992q - 4q^{3} - 8q^{4} - 16q^{6} - 16q^{7} - 4q^{9} + O(q^{10}) \) \( 992q - 4q^{3} - 8q^{4} - 16q^{6} - 16q^{7} - 4q^{9} - 8q^{10} - 4q^{12} - 32q^{13} - 32q^{15} + 24q^{16} - 4q^{18} - 8q^{19} - 8q^{21} - 32q^{22} - 44q^{24} - 8q^{25} - 16q^{27} - 16q^{28} - 36q^{30} - 8q^{33} + 64q^{36} - 8q^{37} - 4q^{39} - 72q^{40} - 68q^{42} - 32q^{43} - 4q^{45} - 8q^{46} - 16q^{48} + 20q^{51} + 16q^{52} - 92q^{54} - 32q^{55} - 16q^{57} + 24q^{58} - 20q^{60} - 8q^{61} - 128q^{64} - 20q^{66} - 72q^{67} - 16q^{69} - 16q^{70} - 4q^{72} - 8q^{73} + 16q^{75} - 32q^{76} + 136q^{78} - 16q^{79} - 48q^{82} + 124q^{84} + 48q^{85} - 4q^{87} - 8q^{88} + 128q^{90} - 64q^{91} - 28q^{93} - 64q^{94} - 72q^{96} - 64q^{97} - 16q^{99} + O(q^{100}) \)

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.ch.a \(992\) \(5.366\) None \(0\) \(-4\) \(0\) \(-16\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database