Properties

Label 672.2.j
Level 672
Weight 2
Character orbit j
Rep. character \(\chi_{672}(239,\cdot)\)
Character field \(\Q\)
Dimension 24
Newforms 4
Sturm bound 256
Trace bound 5

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Defining parameters

Level: \( N \) = \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 672.j (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 24 \)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(256\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 144 24 120
Cusp forms 112 24 88
Eisenstein series 32 0 32

Trace form

\(24q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut +\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 24q^{25} \) \(\mathstrut +\mathstrut 24q^{27} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 24q^{49} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 32q^{67} \) \(\mathstrut +\mathstrut 56q^{75} \) \(\mathstrut +\mathstrut 8q^{81} \) \(\mathstrut -\mathstrut 64q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.j.a \(4\) \(5.366\) \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(0\) \(q+(-1-\zeta_{8}^{2})q^{3}-2\zeta_{8}^{3}q^{5}-\zeta_{8}q^{7}+\cdots\)
672.2.j.b \(4\) \(5.366\) \(\Q(i, \sqrt{5})\) None \(0\) \(2\) \(-4\) \(0\) \(q+(-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}+\cdots\)
672.2.j.c \(4\) \(5.366\) \(\Q(i, \sqrt{5})\) None \(0\) \(2\) \(4\) \(0\) \(q+(-\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
672.2.j.d \(12\) \(5.366\) 12.0.\(\cdots\).2 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+(-\beta _{6}-\beta _{7})q^{5}+\beta _{1}q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(672, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 3}\)