Properties

Label 720.4.h
Level $720$
Weight $4$
Character orbit 720.h
Rep. character $\chi_{720}(431,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $2$
Sturm bound $576$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 720.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(576\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(720, [\chi])\).

Total New Old
Modular forms 456 24 432
Cusp forms 408 24 384
Eisenstein series 48 0 48

Trace form

\( 24 q + O(q^{10}) \) \( 24 q + 144 q^{13} - 600 q^{25} + 1008 q^{37} - 1896 q^{49} + 2160 q^{61} - 432 q^{73} - 1584 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(720, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
720.4.h.a 720.h 12.b $8$ $42.481$ 8.0.\(\cdots\).143 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{5}-\beta _{3}q^{7}+\beta _{6}q^{11}+(22-\beta _{5}+\cdots)q^{13}+\cdots\)
720.4.h.b 720.h 12.b $16$ $42.481$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{5}+(-2\beta _{3}-\beta _{8})q^{7}+(-\beta _{5}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(720, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(720, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)