Properties

Label 560.5.p
Level $560$
Weight $5$
Character orbit 560.p
Rep. character $\chi_{560}(209,\cdot)$
Character field $\Q$
Dimension $94$
Newform subspaces $10$
Sturm bound $480$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 560.p (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(480\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(560, [\chi])\).

Total New Old
Modular forms 396 98 298
Cusp forms 372 94 278
Eisenstein series 24 4 20

Trace form

\( 94 q + 2426 q^{9} + O(q^{10}) \) \( 94 q + 2426 q^{9} + 4 q^{11} + 164 q^{15} - 468 q^{21} - 738 q^{25} + 1052 q^{29} - 958 q^{35} - 2648 q^{39} - 1650 q^{49} + 3976 q^{51} + 3260 q^{65} + 10276 q^{71} + 27268 q^{79} + 44086 q^{81} + 1404 q^{85} + 31108 q^{91} - 25440 q^{95} + 37708 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(560, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
560.5.p.a \(1\) \(57.887\) \(\Q\) \(\Q(\sqrt{-35}) \) \(0\) \(-17\) \(-25\) \(49\) \(q-17q^{3}-5^{2}q^{5}+7^{2}q^{7}+208q^{9}+\cdots\)
560.5.p.b \(1\) \(57.887\) \(\Q\) \(\Q(\sqrt{-35}) \) \(0\) \(17\) \(25\) \(-49\) \(q+17q^{3}+5^{2}q^{5}-7^{2}q^{7}+208q^{9}+\cdots\)
560.5.p.c \(2\) \(57.887\) \(\Q(\sqrt{105}) \) \(\Q(\sqrt{-35}) \) \(0\) \(-17\) \(50\) \(-98\) \(q+(-8-\beta )q^{3}+5^{2}q^{5}-7^{2}q^{7}+(9+\cdots)q^{9}+\cdots\)
560.5.p.d \(2\) \(57.887\) \(\Q(\sqrt{-6}) \) None \(0\) \(-10\) \(10\) \(-70\) \(q-5q^{3}+(5+5\beta )q^{5}+(-35+7\beta )q^{7}+\cdots\)
560.5.p.e \(2\) \(57.887\) \(\Q(\sqrt{-6}) \) None \(0\) \(10\) \(-10\) \(70\) \(q+5q^{3}+(-5-5\beta )q^{5}+(35+7\beta )q^{7}+\cdots\)
560.5.p.f \(2\) \(57.887\) \(\Q(\sqrt{105}) \) \(\Q(\sqrt{-35}) \) \(0\) \(17\) \(-50\) \(98\) \(q+(9-\beta )q^{3}-5^{2}q^{5}+7^{2}q^{7}+(26-17\beta )q^{9}+\cdots\)
560.5.p.g \(8\) \(57.887\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-3\beta _{2}q^{3}+(-\beta _{1}-\beta _{7})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
560.5.p.h \(12\) \(57.887\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{3}+(\beta _{1}+\beta _{7})q^{5}+(\beta _{1}+\beta _{5}+\beta _{8}+\cdots)q^{7}+\cdots\)
560.5.p.i \(16\) \(57.887\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{3}-\beta _{6}q^{5}+\beta _{8}q^{7}+(29-\beta _{10}+\cdots)q^{9}+\cdots\)
560.5.p.j \(48\) \(57.887\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{5}^{\mathrm{old}}(560, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(560, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)