Properties

Label 1120.2.q
Level $1120$
Weight $2$
Character orbit 1120.q
Rep. character $\chi_{1120}(641,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $64$
Newform subspaces $11$
Sturm bound $384$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1120.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 11 \)
Sturm bound: \(384\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1120, [\chi])\).

Total New Old
Modular forms 416 64 352
Cusp forms 352 64 288
Eisenstein series 64 0 64

Trace form

\( 64q - 32q^{9} + O(q^{10}) \) \( 64q - 32q^{9} + 32q^{13} - 40q^{21} - 32q^{25} - 16q^{29} - 16q^{37} - 16q^{41} + 8q^{45} + 32q^{49} + 16q^{53} + 32q^{57} + 48q^{61} + 8q^{65} - 32q^{69} - 16q^{73} + 48q^{77} - 56q^{81} - 40q^{89} + 16q^{93} - 64q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1120, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1120.2.q.a \(2\) \(8.943\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-1\) \(-4\) \(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
1120.2.q.b \(2\) \(8.943\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(1\) \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
1120.2.q.c \(2\) \(8.943\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(1\) \(-1\) \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
1120.2.q.d \(2\) \(8.943\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(-1\) \(4\) \(q+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
1120.2.q.e \(4\) \(8.943\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(-2\) \(-2\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1120.2.q.f \(4\) \(8.943\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(-2\) \(2\) \(q+(1+\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
1120.2.q.g \(8\) \(8.943\) 8.0.49787136.1 None \(0\) \(0\) \(-4\) \(0\) \(q-\beta _{4}q^{3}+(-1+\beta _{2})q^{5}-\beta _{7}q^{7}+2\beta _{4}q^{11}+\cdots\)
1120.2.q.h \(8\) \(8.943\) 8.0.1445900625.1 None \(0\) \(0\) \(4\) \(0\) \(q+\beta _{7}q^{3}-\beta _{3}q^{5}+(\beta _{5}-\beta _{7})q^{7}+(\beta _{3}+\cdots)q^{9}+\cdots\)
1120.2.q.i \(10\) \(8.943\) 10.0.\(\cdots\).1 None \(0\) \(0\) \(5\) \(-2\) \(q-\beta _{5}q^{3}+(1-\beta _{1})q^{5}+\beta _{4}q^{7}+(-2+\cdots)q^{9}+\cdots\)
1120.2.q.j \(10\) \(8.943\) 10.0.\(\cdots\).1 None \(0\) \(0\) \(5\) \(2\) \(q+\beta _{5}q^{3}+(1-\beta _{1})q^{5}-\beta _{4}q^{7}+(-2+\cdots)q^{9}+\cdots\)
1120.2.q.k \(12\) \(8.943\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-6\) \(0\) \(q+\beta _{6}q^{3}+\beta _{2}q^{5}+\beta _{9}q^{7}+(\beta _{1}+2\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1120, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)