Properties

Label 1008.2.k
Level $1008$
Weight $2$
Character orbit 1008.k
Rep. character $\chi_{1008}(881,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $3$
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.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
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 216 16 200
Cusp forms 168 16 152
Eisenstein series 48 0 48

Trace form

\( 16q - 4q^{7} + O(q^{10}) \) \( 16q - 4q^{7} + 32q^{25} - 8q^{43} + 16q^{67} + 48q^{79} - 16q^{85} + 48q^{91} + O(q^{100}) \)

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.k.a \(4\) \(8.049\) \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{7}+(\beta _{1}-\beta _{3})q^{11}+(\beta _{1}+\beta _{3})q^{23}+\cdots\)
1008.2.k.b \(4\) \(8.049\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{3}q^{5}+(1+\beta _{1})q^{7}-\beta _{2}q^{11}-2\beta _{1}q^{13}+\cdots\)
1008.2.k.c \(8\) \(8.049\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(-8\) \(q-\zeta_{16}^{7}q^{5}+(-1-\zeta_{16}^{6})q^{7}+(\zeta_{16}+\cdots)q^{11}+\cdots\)

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

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