Properties

Label 672.2.i
Level 672
Weight 2
Character orbit i
Rep. character \(\chi_{672}(209,\cdot)\)
Character field \(\Q\)
Dimension 28
Newforms 5
Sturm bound 256
Trace bound 7

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Defining parameters

Level: \( N \) = \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 672.i (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 168 \)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(256\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

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

Total New Old
Modular forms 144 36 108
Cusp forms 112 28 84
Eisenstein series 32 8 24

Trace form

\(28q \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut -\mathstrut 20q^{25} \) \(\mathstrut +\mathstrut 16q^{39} \) \(\mathstrut +\mathstrut 4q^{49} \) \(\mathstrut -\mathstrut 16q^{57} \) \(\mathstrut +\mathstrut 36q^{63} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 12q^{81} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.i.a \(4\) \(5.366\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(-4\) \(0\) \(8\) \(q+(-1-\beta _{1})q^{3}+\beta _{1}q^{5}+(2-\beta _{2})q^{7}+\cdots\)
672.2.i.b \(4\) \(5.366\) \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{2}q^{3}+2\beta _{2}q^{5}+(-1+\beta _{3})q^{7}+\cdots\)
672.2.i.c \(4\) \(5.366\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(4\) \(0\) \(8\) \(q+(1-\beta _{1})q^{3}+\beta _{1}q^{5}+(2-\beta _{2})q^{7}+\cdots\)
672.2.i.d \(8\) \(5.366\) 8.0.3317760000.1 None \(0\) \(0\) \(0\) \(-8\) \(q+(-\beta _{2}-\beta _{3})q^{3}-\beta _{3}q^{5}+(-1-\beta _{6}+\cdots)q^{7}+\cdots\)
672.2.i.e \(8\) \(5.366\) 8.0.\(\cdots\).11 \(\Q(\sqrt{-14}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(\beta _{6}-\beta _{7})q^{5}+\beta _{3}q^{7}+(\beta _{2}+\cdots)q^{9}+\cdots\)

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

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