Properties

Label 560.2.q
Level $560$
Weight $2$
Character orbit 560.q
Rep. character $\chi_{560}(81,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $32$
Newform subspaces $12$
Sturm bound $192$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 12 \)
Sturm bound: \(192\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(560, [\chi])\).

Total New Old
Modular forms 216 32 184
Cusp forms 168 32 136
Eisenstein series 48 0 48

Trace form

\( 32q - 4q^{3} - 4q^{7} - 16q^{9} + O(q^{10}) \) \( 32q - 4q^{3} - 4q^{7} - 16q^{9} + 4q^{11} + 4q^{19} + 4q^{21} + 4q^{23} - 16q^{25} + 32q^{27} + 24q^{29} + 16q^{31} - 8q^{37} - 8q^{39} + 8q^{41} - 40q^{43} - 4q^{45} + 20q^{47} - 16q^{49} - 32q^{51} - 16q^{53} - 16q^{55} - 16q^{57} - 8q^{59} - 8q^{61} - 56q^{63} - 4q^{65} + 24q^{67} + 16q^{69} + 32q^{71} + 8q^{73} - 4q^{75} - 24q^{77} + 24q^{79} - 12q^{81} + 112q^{83} + 60q^{87} + 12q^{89} + 24q^{91} - 16q^{93} + 32q^{97} - 88q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(560, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
560.2.q.a \(2\) \(4.472\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(1\) \(-1\) \(q+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
560.2.q.b \(2\) \(4.472\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-1\) \(4\) \(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
560.2.q.c \(2\) \(4.472\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(1\) \(-4\) \(q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
560.2.q.d \(2\) \(4.472\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(1\) \(4\) \(q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
560.2.q.e \(2\) \(4.472\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(-1\) \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
560.2.q.f \(2\) \(4.472\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(1\) \(-5\) \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
560.2.q.g \(2\) \(4.472\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(1\) \(1\) \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
560.2.q.h \(2\) \(4.472\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(1\) \(5\) \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
560.2.q.i \(2\) \(4.472\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(1\) \(-1\) \(q+(3-3\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
560.2.q.j \(4\) \(4.472\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(-2\) \(2\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
560.2.q.k \(4\) \(4.472\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(-2\) \(-2\) \(q+(1+\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
560.2.q.l \(6\) \(4.472\) 6.0.11337408.1 None \(0\) \(0\) \(-3\) \(-6\) \(q+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}-\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(560, [\chi])\) into lower level spaces

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