Properties

Label 1008.4.bt
Level $1008$
Weight $4$
Character orbit 1008.bt
Rep. character $\chi_{1008}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $4$
Sturm bound $768$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.bt (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(768\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1008, [\chi])\).

Total New Old
Modular forms 1200 96 1104
Cusp forms 1104 96 1008
Eisenstein series 96 0 96

Trace form

\( 96q + 36q^{7} + O(q^{10}) \) \( 96q + 36q^{7} - 540q^{19} - 1368q^{25} + 180q^{31} + 168q^{43} + 768q^{49} + 1164q^{67} + 648q^{73} - 1884q^{79} + 2592q^{85} + 948q^{91} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1008.4.bt.a \(16\) \(59.474\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-56\) \(q-\beta _{13}q^{5}+(-3+\beta _{4})q^{7}+(-\beta _{1}-3\beta _{6}+\cdots)q^{11}+\cdots\)
1008.4.bt.b \(16\) \(59.474\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{9}q^{5}+(-1-2\beta _{1}+\beta _{6}+\beta _{8})q^{7}+\cdots\)
1008.4.bt.c \(16\) \(59.474\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(64\) \(q+(-\beta _{10}+\beta _{12})q^{5}+(6-3\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1008.4.bt.d \(48\) \(59.474\) None \(0\) \(0\) \(0\) \(24\)

Decomposition of \(S_{4}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)