Properties

Label 480.2.f
Level $480$
Weight $2$
Character orbit 480.f
Rep. character $\chi_{480}(289,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $5$
Sturm bound $192$
Trace bound $15$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 480.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(192\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(7\), \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(480, [\chi])\).

Total New Old
Modular forms 112 12 100
Cusp forms 80 12 68
Eisenstein series 32 0 32

Trace form

\( 12 q - 4 q^{5} - 12 q^{9} + O(q^{10}) \) \( 12 q - 4 q^{5} - 12 q^{9} - 20 q^{25} + 8 q^{29} + 40 q^{41} + 4 q^{45} - 12 q^{49} - 8 q^{61} + 12 q^{81} - 64 q^{85} - 40 q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(480, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
480.2.f.a 480.f 5.b $2$ $3.833$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-2+i)q^{5}-2iq^{7}-q^{9}+\cdots\)
480.2.f.b 480.f 5.b $2$ $3.833$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-2-i)q^{5}-2iq^{7}-q^{9}+\cdots\)
480.2.f.c 480.f 5.b $2$ $3.833$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(1+2i)q^{5}+4iq^{7}-q^{9}+\cdots\)
480.2.f.d 480.f 5.b $2$ $3.833$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(1-2i)q^{5}+4iq^{7}-q^{9}+\cdots\)
480.2.f.e 480.f 5.b $4$ $3.833$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{2}q^{5}-2\beta _{1}q^{7}-q^{9}-2\beta _{3}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(480, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(480, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)