Properties

Label 280.2.h
Level 280280
Weight 22
Character orbit 280.h
Rep. character χ280(251,)\chi_{280}(251,\cdot)
Character field Q\Q
Dimension 3232
Newform subspaces 22
Sturm bound 9696
Trace bound 55

Related objects

Downloads

Learn more

Defining parameters

Level: N N == 280=2357 280 = 2^{3} \cdot 5 \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 280.h (of order 22 and degree 11)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 56 56
Character field: Q\Q
Newform subspaces: 2 2
Sturm bound: 9696
Trace bound: 55
Distinguishing TpT_p: 1313

Dimensions

The following table gives the dimensions of various subspaces of M2(280,[χ])M_{2}(280, [\chi]).

Total New Old
Modular forms 52 32 20
Cusp forms 44 32 12
Eisenstein series 8 0 8

Trace form

32q+2q2+2q4+2q832q98q11+6q14+18q1630q18+12q22+32q252q2838q32+30q36+64q428q4340q44+12q4616q49++40q99+O(q100) 32 q + 2 q^{2} + 2 q^{4} + 2 q^{8} - 32 q^{9} - 8 q^{11} + 6 q^{14} + 18 q^{16} - 30 q^{18} + 12 q^{22} + 32 q^{25} - 2 q^{28} - 38 q^{32} + 30 q^{36} + 64 q^{42} - 8 q^{43} - 40 q^{44} + 12 q^{46} - 16 q^{49}+ \cdots + 40 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(280,[χ])S_{2}^{\mathrm{new}}(280, [\chi]) into newform subspaces

Label Char Prim Dim AA Field CM Minimal twist Traces Sato-Tate qq-expansion
a2a_{2} a3a_{3} a5a_{5} a7a_{7}
280.2.h.a 280.h 56.e 1616 2.2362.236 Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots) None 280.2.h.a 11 00 16-16 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β5q2+β4q3+β9q4q5+β6q6+q+\beta _{5}q^{2}+\beta _{4}q^{3}+\beta _{9}q^{4}-q^{5}+\beta _{6}q^{6}+\cdots
280.2.h.b 280.h 56.e 1616 2.2362.236 Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots) None 280.2.h.a 11 00 1616 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+β5q2β4q3+β9q4+q5β6q6+q+\beta _{5}q^{2}-\beta _{4}q^{3}+\beta _{9}q^{4}+q^{5}-\beta _{6}q^{6}+\cdots

Decomposition of S2old(280,[χ])S_{2}^{\mathrm{old}}(280, [\chi]) into lower level spaces

S2old(280,[χ]) S_{2}^{\mathrm{old}}(280, [\chi]) \simeq S2new(56,[χ])S_{2}^{\mathrm{new}}(56, [\chi])2^{\oplus 2}