Properties

Label 7056.2.k
Level $7056$
Weight $2$
Character orbit 7056.k
Rep. character $\chi_{7056}(881,\cdot)$
Character field $\Q$
Dimension $80$
Newform subspaces $9$
Sturm bound $2688$
Trace bound $121$

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Defining parameters

Level: \( N \) \(=\) \( 7056 = 2^{4} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7056.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(2688\)
Trace bound: \(121\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(7056, [\chi])\).

Total New Old
Modular forms 1440 80 1360
Cusp forms 1248 80 1168
Eisenstein series 192 0 192

Trace form

\( 80q + O(q^{10}) \) \( 80q + 64q^{25} + 8q^{43} - 24q^{67} - 40q^{79} + 32q^{85} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(7056, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
7056.2.k.a \(4\) \(56.342\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}-\beta _{3}q^{11}-\beta _{1}q^{13}+2\beta _{2}q^{17}+\cdots\)
7056.2.k.b \(4\) \(56.342\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{5}-\beta _{1}q^{11}-3\beta _{2}q^{13}+2\beta _{3}q^{17}+\cdots\)
7056.2.k.c \(8\) \(56.342\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{5}q^{5}-\zeta_{16}q^{11}-3\zeta_{16}^{2}q^{13}+\cdots\)
7056.2.k.d \(8\) \(56.342\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{5}q^{5}-2\zeta_{16}q^{11}+(-4\zeta_{16}^{2}+\cdots)q^{13}+\cdots\)
7056.2.k.e \(8\) \(56.342\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{5}q^{5}+\zeta_{16}q^{11}+(2\zeta_{16}^{2}+\zeta_{16}^{4}+\cdots)q^{13}+\cdots\)
7056.2.k.f \(8\) \(56.342\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{5}+\zeta_{24}^{7}q^{11}-\zeta_{24}^{3}q^{13}+\cdots\)
7056.2.k.g \(8\) \(56.342\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{4}q^{5}+(\zeta_{16}+2\zeta_{16}^{2})q^{11}-\zeta_{16}^{5}q^{13}+\cdots\)
7056.2.k.h \(16\) \(56.342\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{13}q^{5}-\beta _{6}q^{11}+(-2\beta _{3}+2\beta _{5}+\cdots)q^{13}+\cdots\)
7056.2.k.i \(16\) \(56.342\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{13}q^{5}+(\beta _{5}-\beta _{6})q^{11}+\beta _{7}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(7056, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(7056, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1764, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2352, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3528, [\chi])\)\(^{\oplus 2}\)