Properties

Label 240.2.bk
Level 240240
Weight 22
Character orbit 240.bk
Rep. character χ240(11,)\chi_{240}(11,\cdot)
Character field Q(ζ4)\Q(\zeta_{4})
Dimension 6464
Newform subspaces 22
Sturm bound 9696
Trace bound 11

Related objects

Downloads

Learn more

Defining parameters

Level: N N == 240=2435 240 = 2^{4} \cdot 3 \cdot 5
Weight: k k == 2 2
Character orbit: [χ][\chi] == 240.bk (of order 44 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 48 48
Character field: Q(i)\Q(i)
Newform subspaces: 2 2
Sturm bound: 9696
Trace bound: 11
Distinguishing TpT_p: 77

Dimensions

The following table gives the dimensions of various subspaces of M2(240,[χ])M_{2}(240, [\chi]).

Total New Old
Modular forms 104 64 40
Cusp forms 88 64 24
Eisenstein series 16 0 16

Trace form

64q+12q64q10+12q1236q1620q18+8q1924q2236q2424q2724q284q34+12q3648q39+20q42+60q46+40q48+64q49++32q99+O(q100) 64 q + 12 q^{6} - 4 q^{10} + 12 q^{12} - 36 q^{16} - 20 q^{18} + 8 q^{19} - 24 q^{22} - 36 q^{24} - 24 q^{27} - 24 q^{28} - 4 q^{34} + 12 q^{36} - 48 q^{39} + 20 q^{42} + 60 q^{46} + 40 q^{48} + 64 q^{49}+ \cdots + 32 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(240,[χ])S_{2}^{\mathrm{new}}(240, [\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}
240.2.bk.a 240.bk 48.k 44 1.9161.916 Q(ζ8)\Q(\zeta_{8}) None 240.2.bk.a 00 4-4 00 16-16 SU(2)[C4]\mathrm{SU}(2)[C_{4}] q+(ζ8+ζ83)q2+(1ζ82ζ83)q3+q+(\zeta_{8}+\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\cdots
240.2.bk.b 240.bk 48.k 6060 1.9161.916 None 240.2.bk.b 00 44 00 1616 SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Decomposition of S2old(240,[χ])S_{2}^{\mathrm{old}}(240, [\chi]) into lower level spaces

S2old(240,[χ]) S_{2}^{\mathrm{old}}(240, [\chi]) \simeq S2new(48,[χ])S_{2}^{\mathrm{new}}(48, [\chi])2^{\oplus 2}