Properties

Label 672.2.q
Level $672$
Weight $2$
Character orbit 672.q
Rep. character $\chi_{672}(193,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $32$
Newform subspaces $12$
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.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 12 \)
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 288 32 256
Cusp forms 224 32 192
Eisenstein series 64 0 64

Trace form

\( 32q - 16q^{9} + O(q^{10}) \) \( 32q - 16q^{9} + 16q^{13} - 16q^{21} - 8q^{25} + 8q^{33} - 8q^{37} - 32q^{41} + 32q^{49} + 16q^{53} + 16q^{57} + 32q^{61} + 16q^{65} - 24q^{73} + 32q^{77} - 16q^{81} + 128q^{85} - 32q^{89} - 24q^{93} + 16q^{97} + O(q^{100}) \)

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.q.a \(2\) \(5.366\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-3\) \(1\) \(q+(-1+\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
672.2.q.b \(2\) \(5.366\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-1\) \(-5\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
672.2.q.c \(2\) \(5.366\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(1\) \(q+(-1+\zeta_{6})q^{3}+(2-3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
672.2.q.d \(2\) \(5.366\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(5\) \(q+(-1+\zeta_{6})q^{3}+(2+\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
672.2.q.e \(2\) \(5.366\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(4\) \(5\) \(q+(-1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
672.2.q.f \(2\) \(5.366\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-3\) \(-1\) \(q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
672.2.q.g \(2\) \(5.366\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-1\) \(5\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
672.2.q.h \(2\) \(5.366\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-5\) \(q+(1-\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
672.2.q.i \(2\) \(5.366\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-1\) \(q+(1-\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
672.2.q.j \(2\) \(5.366\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(4\) \(-5\) \(q+(1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
672.2.q.k \(6\) \(5.366\) 6.0.1156923.1 None \(0\) \(-3\) \(0\) \(-3\) \(q+\beta _{2}q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
672.2.q.l \(6\) \(5.366\) 6.0.1156923.1 None \(0\) \(3\) \(0\) \(3\) \(q-\beta _{2}q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(672, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)