↑

Properties

Label 980.2.k
Level $980$
Weight $2$
Character orbit 980.k
Rep. character $\chi_{980}(687,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $226$
Newform subspaces $13$
Sturm bound $336$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 13 \)
Sturm bound: \(336\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(980, [\chi])\).

Total New Old
Modular forms 368 266 102
Cusp forms 304 226 78
Eisenstein series 64 40 24

Trace form

\( 226 q + 2 q^{2} + 4 q^{5} + 8 q^{6} - 16 q^{8} + O(q^{10}) \) \( 226 q + 2 q^{2} + 4 q^{5} + 8 q^{6} - 16 q^{8} + 10 q^{10} + 16 q^{12} + 6 q^{13} + 16 q^{16} + 14 q^{17} + 2 q^{18} - 16 q^{20} - 16 q^{22} + 14 q^{25} + 28 q^{26} - 16 q^{30} - 28 q^{32} - 36 q^{36} - 6 q^{37} + 40 q^{40} + 16 q^{41} - 26 q^{45} - 40 q^{46} + 24 q^{48} - 18 q^{50} - 12 q^{52} + 26 q^{53} - 24 q^{57} + 20 q^{58} - 60 q^{60} + 40 q^{61} - 40 q^{62} - 22 q^{65} - 32 q^{66} - 68 q^{68} - 84 q^{72} - 30 q^{73} - 8 q^{76} - 32 q^{78} + 4 q^{80} - 18 q^{81} - 72 q^{82} + 14 q^{85} - 32 q^{86} + 64 q^{88} + 10 q^{90} + 44 q^{92} + 24 q^{93} - 120 q^{96} - 46 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(980, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
980.2.k.a 980.k 20.e $2$ $7.825$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(-2\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1-i)q^{2}+2iq^{4}+(2-i)q^{5}+\cdots\)
980.2.k.b 980.k 20.e $2$ $7.825$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(2\) \(0\) \(-2\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1+i)q^{2}+2iq^{4}+(-1-2i)q^{5}+\cdots\)
980.2.k.c 980.k 20.e $2$ $7.825$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(2\) \(0\) \(2\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1+i)q^{2}+2iq^{4}+(1+2i)q^{5}+(-2+\cdots)q^{8}+\cdots\)
980.2.k.d 980.k 20.e $4$ $7.825$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) \(-4\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1+\zeta_{8}^{2})q^{2}-2\zeta_{8}^{2}q^{4}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots\)
980.2.k.e 980.k 20.e $4$ $7.825$ \(\Q(i, \sqrt{14})\) None \(4\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{2})q^{2}+\beta _{1}q^{3}+2\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
980.2.k.f 980.k 20.e $4$ $7.825$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) \(4\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1-\zeta_{8}^{2})q^{2}-2\zeta_{8}^{2}q^{4}+(-2\zeta_{8}+\cdots)q^{5}+\cdots\)
980.2.k.g 980.k 20.e $4$ $7.825$ \(\Q(i, \sqrt{14})\) None \(4\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{2})q^{2}+\beta _{1}q^{3}+2\beta _{2}q^{4}+(1+\cdots)q^{5}+\cdots\)
980.2.k.h 980.k 20.e $8$ $7.825$ \(\Q(\zeta_{24})\) None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\zeta_{24}^{3}-\zeta_{24}^{6})q^{2}+(-\zeta_{24}^{4}-\zeta_{24}^{7})q^{3}+\cdots\)
980.2.k.i 980.k 20.e $32$ $7.825$ None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
980.2.k.j 980.k 20.e $36$ $7.825$ None \(-2\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$
980.2.k.k 980.k 20.e $36$ $7.825$ None \(-2\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$
980.2.k.l 980.k 20.e $36$ $7.825$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
980.2.k.m 980.k 20.e $56$ $7.825$ None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(980, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(980, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)