Properties

Label 720.2.o
Level $720$
Weight $2$
Character orbit 720.o
Rep. character $\chi_{720}(719,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $2$
Sturm bound $288$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.o (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 60 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 168 12 156
Cusp forms 120 12 108
Eisenstein series 48 0 48

Trace form

\( 12 q + O(q^{10}) \) \( 12 q + 24 q^{25} + 60 q^{49} + 24 q^{61} - 60 q^{85} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
720.2.o.a 720.o 60.h $4$ $5.749$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{8}^{3}q^{5}+2\zeta_{8}q^{13}+(\zeta_{8}^{2}-2\zeta_{8}^{3})q^{17}+\cdots\)
720.2.o.b 720.o 60.h $8$ $5.749$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\zeta_{24}-\zeta_{24}^{2})q^{5}-\zeta_{24}^{6}q^{7}+\zeta_{24}^{3}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(720, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)