Properties

Label 672.2.h
Level $672$
Weight $2$
Character orbit 672.h
Rep. character $\chi_{672}(575,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $5$
Sturm bound $256$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 672.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(256\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\)

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

\( 24q - 8q^{9} + O(q^{10}) \) \( 24q - 8q^{9} - 24q^{25} + 32q^{33} - 32q^{37} - 48q^{45} - 24q^{49} - 32q^{57} + 32q^{61} + 48q^{69} + 48q^{73} - 8q^{81} + 16q^{85} + 48q^{93} - 48q^{97} + O(q^{100}) \)

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.h.a \(4\) \(5.366\) \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(0\) \(q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
672.2.h.b \(4\) \(5.366\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-3\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots\)
672.2.h.c \(4\) \(5.366\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots\)
672.2.h.d \(4\) \(5.366\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(0\) \(q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
672.2.h.e \(8\) \(5.366\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}-\beta _{4}q^{5}+\beta _{1}q^{7}+(-2+\beta _{6}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(672, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)