Properties

Label 672.2.b
Level 672
Weight 2
Character orbit b
Rep. character \(\chi_{672}(223,\cdot)\)
Character field \(\Q\)
Dimension 16
Newforms 2
Sturm bound 256
Trace bound 3

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Defining parameters

Level: \( N \) = \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 672.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 28 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(256\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(19\)

Dimensions

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

Total New Old
Modular forms 144 16 128
Cusp forms 112 16 96
Eisenstein series 32 0 32

Trace form

\( 16q + 16q^{9} + O(q^{10}) \) \( 16q + 16q^{9} + 8q^{21} - 32q^{25} + 16q^{37} + 32q^{53} + 16q^{57} + 32q^{65} + 64q^{77} + 16q^{81} - 112q^{85} - 32q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(672, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
672.2.b.a \(8\) \(5.366\) 8.0.836829184.2 None \(0\) \(-8\) \(0\) \(-4\) \(q-q^{3}+\beta _{1}q^{5}+\beta _{4}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
672.2.b.b \(8\) \(5.366\) 8.0.836829184.2 None \(0\) \(8\) \(0\) \(4\) \(q+q^{3}-\beta _{1}q^{5}+\beta _{2}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(672, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(672, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)