Properties

Label 720.2.f
Level $720$
Weight $2$
Character orbit 720.f
Rep. character $\chi_{720}(289,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $7$
Sturm bound $288$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(288\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\)

Dimensions

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

Total New Old
Modular forms 168 16 152
Cusp forms 120 14 106
Eisenstein series 48 2 46

Trace form

\( 14 q + O(q^{10}) \) \( 14 q - 8 q^{11} + 2 q^{25} + 8 q^{29} - 8 q^{31} + 16 q^{35} + 8 q^{41} - 22 q^{49} + 32 q^{55} + 8 q^{59} + 4 q^{61} - 8 q^{65} + 32 q^{71} - 8 q^{79} + 12 q^{85} - 16 q^{89} + 32 q^{91} - 40 q^{95} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
720.2.f.a 720.f 5.b $2$ $5.749$ \(\Q(\sqrt{-1}) \) None 360.2.f.b \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2+i)q^{5}+4iq^{7}-4q^{11}-4iq^{13}+\cdots\)
720.2.f.b 720.f 5.b $2$ $5.749$ \(\Q(\sqrt{-1}) \) None 120.2.f.a \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2+i)q^{5}-2iq^{7}+2q^{11}+2iq^{13}+\cdots\)
720.2.f.c 720.f 5.b $2$ $5.749$ \(\Q(\sqrt{-1}) \) None 60.2.d.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+i)q^{5}-2iq^{7}-4q^{11}-2iq^{17}+\cdots\)
720.2.f.d 720.f 5.b $2$ $5.749$ \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{-15}) \) 45.2.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{5}+2\beta q^{17}+4q^{19}+4\beta q^{23}+\cdots\)
720.2.f.e 720.f 5.b $2$ $5.749$ \(\Q(\sqrt{-1}) \) None 40.2.c.a \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{5}+iq^{7}-4q^{11}+2iq^{13}+\cdots\)
720.2.f.f 720.f 5.b $2$ $5.749$ \(\Q(\sqrt{-1}) \) None 30.2.c.a \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2+i)q^{5}-2iq^{7}+2q^{11}-6iq^{13}+\cdots\)
720.2.f.g 720.f 5.b $2$ $5.749$ \(\Q(\sqrt{-1}) \) None 360.2.f.b \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2+i)q^{5}-4iq^{7}+4q^{11}+4iq^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(720, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)