Properties

Label 1008.2.cz
Level $1008$
Weight $2$
Character orbit 1008.cz
Rep. character $\chi_{1008}(367,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $9$
Sturm bound $384$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.cz (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 252 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 9 \)
Sturm bound: \(384\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1008, [\chi])\).

Total New Old
Modular forms 408 96 312
Cusp forms 360 96 264
Eisenstein series 48 0 48

Trace form

\( 96 q + O(q^{10}) \) \( 96 q + 12 q^{21} + 48 q^{25} - 12 q^{29} + 36 q^{45} - 24 q^{57} - 48 q^{65} - 24 q^{77} + 48 q^{81} + 36 q^{89} - 24 q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1008.2.cz.a \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(-1\) \(q+(-2+\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}+(3+\cdots)q^{9}+\cdots\)
1008.2.cz.b \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(-4\) \(q+(1-2\zeta_{6})q^{3}+(-1-\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1008.2.cz.c \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(4\) \(q+(-1+2\zeta_{6})q^{3}+(-1-\zeta_{6})q^{5}+(1+\cdots)q^{7}+\cdots\)
1008.2.cz.d \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(1\) \(q+(2-\zeta_{6})q^{3}+(2-3\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots\)
1008.2.cz.e \(4\) \(8.049\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(6\) \(-4\) \(q+(1+2\beta _{1})q^{3}+(2+\beta _{1}+\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1008.2.cz.f \(4\) \(8.049\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(6\) \(4\) \(q+(-1-2\beta _{1})q^{3}+(2+\beta _{1}+\beta _{3})q^{5}+\cdots\)
1008.2.cz.g \(24\) \(8.049\) None \(0\) \(-3\) \(-3\) \(4\)
1008.2.cz.h \(24\) \(8.049\) None \(0\) \(3\) \(-3\) \(-4\)
1008.2.cz.i \(32\) \(8.049\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)