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Properties

Label 720.2.cu
Level $720$
Weight $2$
Character orbit 720.cu
Rep. character $\chi_{720}(113,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $136$
Newform subspaces $5$
Sturm bound $288$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.cu (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 5 \)
Sturm bound: \(288\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 624 152 472
Cusp forms 528 136 392
Eisenstein series 96 16 80

Trace form

\( 136 q + 4 q^{3} - 6 q^{5} + 2 q^{7} + O(q^{10}) \) \( 136 q + 4 q^{3} - 6 q^{5} + 2 q^{7} + 12 q^{11} - 2 q^{13} - 8 q^{15} + 6 q^{23} - 2 q^{25} + 28 q^{27} + 4 q^{31} - 10 q^{33} - 8 q^{37} - 12 q^{41} + 2 q^{43} + 6 q^{45} + 42 q^{47} + 32 q^{51} + 28 q^{55} - 8 q^{57} - 4 q^{61} + 54 q^{63} - 54 q^{65} + 2 q^{67} - 8 q^{73} - 40 q^{75} - 6 q^{77} - 16 q^{81} + 6 q^{83} - 2 q^{85} + 26 q^{87} + 16 q^{91} + 2 q^{93} - 24 q^{95} - 2 q^{97} + O(q^{100}) \)

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.cu.a 720.cu 45.l $8$ $5.749$ \(\Q(\zeta_{24})\) None \(0\) \(-4\) \(12\) \(8\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1-\zeta_{24}^{2}+\zeta_{24}^{4}-\zeta_{24}^{5})q^{3}+\cdots\)
720.2.cu.b 720.cu 45.l $16$ $5.749$ 16.0.\(\cdots\).9 None \(0\) \(0\) \(-12\) \(-8\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1-\beta _{1}+\beta _{2}-\beta _{4}+2\beta _{6}-\beta _{7}+\cdots)q^{3}+\cdots\)
720.2.cu.c 720.cu 45.l $16$ $5.749$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(6\) \(-6\) \(2\) $\mathrm{SU}(2)[C_{12}]$ \(q-\beta _{7}q^{3}+(-\beta _{6}+\beta _{13})q^{5}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
720.2.cu.d 720.cu 45.l $24$ $5.749$ None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
720.2.cu.e 720.cu 45.l $72$ $5.749$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

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

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