↑

Properties

Label 720.2.t
Level $720$
Weight $2$
Character orbit 720.t
Rep. character $\chi_{720}(181,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $80$
Newform subspaces $5$
Sturm bound $288$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 5 \)
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 304 80 224
Cusp forms 272 80 192
Eisenstein series 32 0 32

Trace form

\( 80 q - 4 q^{4} + O(q^{10}) \) \( 80 q - 4 q^{4} - 4 q^{10} - 8 q^{11} + 4 q^{14} + 8 q^{16} + 8 q^{19} + 8 q^{20} + 28 q^{22} + 16 q^{26} + 44 q^{28} - 16 q^{29} + 40 q^{32} + 24 q^{34} - 16 q^{37} + 20 q^{38} + 8 q^{43} - 48 q^{44} - 60 q^{46} + 40 q^{47} - 80 q^{49} - 4 q^{50} - 56 q^{52} + 16 q^{53} - 64 q^{56} + 4 q^{58} + 40 q^{59} - 16 q^{61} + 56 q^{62} - 64 q^{64} + 8 q^{67} + 56 q^{68} - 8 q^{70} + 40 q^{74} + 56 q^{76} + 16 q^{77} - 16 q^{79} - 16 q^{80} + 4 q^{82} - 40 q^{83} + 16 q^{85} - 76 q^{86} - 64 q^{88} - 64 q^{91} - 52 q^{92} + 4 q^{94} - 32 q^{95} - 76 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.t.a 720.t 16.e $4$ $5.749$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+\zeta_{8}q^{5}+\cdots\)
720.2.t.b 720.t 16.e $8$ $5.749$ 8.0.18939904.2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta _{4}-\beta _{5})q^{2}+(-1+\beta _{2}-\beta _{3}-\beta _{6}+\cdots)q^{4}+\cdots\)
720.2.t.c 720.t 16.e $16$ $5.749$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{9}q^{2}+(\beta _{1}-\beta _{5}-\beta _{14})q^{4}-\beta _{4}q^{5}+\cdots\)
720.2.t.d 720.t 16.e $20$ $5.749$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{3}q^{5}+(-1+\beta _{2}+\cdots)q^{7}+\cdots\)
720.2.t.e 720.t 16.e $32$ $5.749$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(720, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)