Properties

Label 720.2.q
Level $720$
Weight $2$
Character orbit 720.q
Rep. character $\chi_{720}(241,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $48$
Newform subspaces $12$
Sturm bound $288$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 12 \)
Sturm bound: \(288\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(720, [\chi])\).

Total New Old
Modular forms 312 48 264
Cusp forms 264 48 216
Eisenstein series 48 0 48

Trace form

\( 48q + 4q^{9} + O(q^{10}) \) \( 48q + 4q^{9} + 8q^{17} + 4q^{21} + 12q^{23} - 24q^{25} + 12q^{27} - 4q^{29} - 12q^{31} + 12q^{33} + 24q^{35} + 36q^{39} + 4q^{41} - 12q^{43} - 8q^{45} + 20q^{47} - 24q^{49} + 8q^{51} - 12q^{57} - 12q^{59} - 40q^{63} - 28q^{69} - 24q^{71} + 24q^{73} - 16q^{77} - 8q^{81} - 56q^{83} - 60q^{87} - 24q^{89} + 24q^{91} - 8q^{93} + 16q^{95} - 12q^{97} + 76q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(720, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
720.2.q.a \(2\) \(5.749\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(-1\) \(-1\) \(q+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
720.2.q.b \(2\) \(5.749\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(1\) \(-1\) \(q+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
720.2.q.c \(2\) \(5.749\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-1\) \(-4\) \(q+(1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+\cdots\)
720.2.q.d \(2\) \(5.749\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(1\) \(-3\) \(q+(2-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+\cdots\)
720.2.q.e \(2\) \(5.749\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(1\) \(0\) \(q+(1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(-5+\cdots)q^{11}+\cdots\)
720.2.q.f \(4\) \(5.749\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(-2\) \(2\) \(1\) \(q+(-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
720.2.q.g \(4\) \(5.749\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(-2\) \(2\) \(2\) \(q+(\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\beta _{2}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
720.2.q.h \(4\) \(5.749\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(4\) \(q-\zeta_{12}^{2}q^{3}+\zeta_{12}q^{5}+(2-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
720.2.q.i \(6\) \(5.749\) 6.0.954288.1 None \(0\) \(-1\) \(-3\) \(5\) \(q-\beta _{4}q^{3}+\beta _{3}q^{5}+(2-\beta _{1}+\beta _{2}+2\beta _{3}+\cdots)q^{7}+\cdots\)
720.2.q.j \(6\) \(5.749\) 6.0.954288.1 None \(0\) \(1\) \(-3\) \(-5\) \(q+(\beta _{2}-\beta _{5})q^{3}+\beta _{3}q^{5}+(-2-2\beta _{3}+\cdots)q^{7}+\cdots\)
720.2.q.k \(6\) \(5.749\) 6.0.954288.1 None \(0\) \(1\) \(3\) \(3\) \(q-\beta _{4}q^{3}+(1+\beta _{2})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
720.2.q.l \(8\) \(5.749\) 8.0.856615824.2 None \(0\) \(0\) \(-4\) \(-1\) \(q+\beta _{4}q^{3}-\beta _{1}q^{5}+(\beta _{2}-\beta _{4})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(720, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(720, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)