Properties

Label 1008.2.df
Level $1008$
Weight $2$
Character orbit 1008.df
Rep. character $\chi_{1008}(689,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $92$
Newform subspaces $5$
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.df (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(384\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 408 100 308
Cusp forms 360 92 268
Eisenstein series 48 8 40

Trace form

\( 92q + 3q^{3} - 6q^{5} + q^{7} - q^{9} + O(q^{10}) \) \( 92q + 3q^{3} - 6q^{5} + q^{7} - q^{9} + 7q^{15} + 6q^{19} - 4q^{21} + 74q^{25} + 6q^{29} - 15q^{31} - 3q^{33} + 15q^{35} - 2q^{37} + 19q^{39} + 8q^{43} - 15q^{45} + 3q^{47} - q^{49} + 3q^{51} - 2q^{57} + 3q^{59} - 3q^{61} - 7q^{63} - 27q^{65} - q^{67} + 9q^{69} - 6q^{73} + 18q^{75} - 27q^{77} - q^{79} + 3q^{81} + 30q^{83} + 3q^{85} + 66q^{87} + 12q^{89} + 12q^{91} - 23q^{93} + 87q^{95} + 43q^{99} + O(q^{100}) \)

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.df.a \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-6\) \(5\) \(q+(2-\zeta_{6})q^{3}-3q^{5}+(3-\zeta_{6})q^{7}+(3+\cdots)q^{9}+\cdots\)
1008.2.df.b \(10\) \(8.049\) 10.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(-3\) \(q+(\beta _{1}-\beta _{2}+\beta _{4}+\beta _{7}+\beta _{8}-\beta _{9})q^{3}+\cdots\)
1008.2.df.c \(16\) \(8.049\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-2\) \(q-\beta _{3}q^{3}-\beta _{11}q^{5}+(1-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
1008.2.df.d \(16\) \(8.049\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(1\) \(q+(-\beta _{3}-\beta _{12})q^{3}+(-\beta _{7}+\beta _{9})q^{5}+\cdots\)
1008.2.df.e \(48\) \(8.049\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)