Properties

Label 70.4.c
Level 7070
Weight 44
Character orbit 70.c
Rep. character χ70(29,)\chi_{70}(29,\cdot)
Character field Q\Q
Dimension 88
Newform subspaces 22
Sturm bound 4848
Trace bound 11

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Defining parameters

Level: N N == 70=257 70 = 2 \cdot 5 \cdot 7
Weight: k k == 4 4
Character orbit: [χ][\chi] == 70.c (of order 22 and degree 11)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 5 5
Character field: Q\Q
Newform subspaces: 2 2
Sturm bound: 4848
Trace bound: 11
Distinguishing TpT_p: 33

Dimensions

The following table gives the dimensions of various subspaces of M4(70,[χ])M_{4}(70, [\chi]).

Total New Old
Modular forms 40 8 32
Cusp forms 32 8 24
Eisenstein series 8 0 8

Trace form

8q32q4+4q5196q956q1036q11+56q14+40q15+128q1696q1916q20196q21+636q25+368q26+316q29200q30+72q31784q34++8184q99+O(q100) 8 q - 32 q^{4} + 4 q^{5} - 196 q^{9} - 56 q^{10} - 36 q^{11} + 56 q^{14} + 40 q^{15} + 128 q^{16} - 96 q^{19} - 16 q^{20} - 196 q^{21} + 636 q^{25} + 368 q^{26} + 316 q^{29} - 200 q^{30} + 72 q^{31} - 784 q^{34}+ \cdots + 8184 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S4new(70,[χ])S_{4}^{\mathrm{new}}(70, [\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}
70.4.c.a 70.c 5.b 22 4.1304.130 Q(1)\Q(\sqrt{-1}) None 70.4.c.a 00 00 2020 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+2iq2+7iq34q4+(5i+10)q5+q+2 i q^{2}+7 i q^{3}-4 q^{4}+(5 i+10)q^{5}+\cdots
70.4.c.b 70.c 5.b 66 4.1304.130 6.0.\cdots.1 None 70.4.c.b 00 00 16-16 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+2β3q2+(2β3+β5)q34q4+q+2\beta _{3}q^{2}+(-2\beta _{3}+\beta _{5})q^{3}-4q^{4}+\cdots

Decomposition of S4old(70,[χ])S_{4}^{\mathrm{old}}(70, [\chi]) into lower level spaces

S4old(70,[χ]) S_{4}^{\mathrm{old}}(70, [\chi]) \simeq S4new(10,[χ])S_{4}^{\mathrm{new}}(10, [\chi])2^{\oplus 2}\oplusS4new(35,[χ])S_{4}^{\mathrm{new}}(35, [\chi])2^{\oplus 2}