Properties

Label 112.4.i
Level 112112
Weight 44
Character orbit 112.i
Rep. character χ112(65,)\chi_{112}(65,\cdot)
Character field Q(ζ3)\Q(\zeta_{3})
Dimension 2222
Newform subspaces 66
Sturm bound 6464
Trace bound 33

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Defining parameters

Level: N N == 112=247 112 = 2^{4} \cdot 7
Weight: k k == 4 4
Character orbit: [χ][\chi] == 112.i (of order 33 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 7 7
Character field: Q(ζ3)\Q(\zeta_{3})
Newform subspaces: 6 6
Sturm bound: 6464
Trace bound: 33
Distinguishing TpT_p: 33

Dimensions

The following table gives the dimensions of various subspaces of M4(112,[χ])M_{4}(112, [\chi]).

Total New Old
Modular forms 108 26 82
Cusp forms 84 22 62
Eisenstein series 24 4 20

Trace form

22q5q3q5+20q782q99q114q1350q15q17203q19+93q2139q23260q25+382q27+140q29+307q31+65q33357q35+5636q99+O(q100) 22 q - 5 q^{3} - q^{5} + 20 q^{7} - 82 q^{9} - 9 q^{11} - 4 q^{13} - 50 q^{15} - q^{17} - 203 q^{19} + 93 q^{21} - 39 q^{23} - 260 q^{25} + 382 q^{27} + 140 q^{29} + 307 q^{31} + 65 q^{33} - 357 q^{35}+ \cdots - 5636 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S4new(112,[χ])S_{4}^{\mathrm{new}}(112, [\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}
112.4.i.a 112.i 7.c 22 6.6086.608 Q(3)\Q(\sqrt{-3}) None 14.4.c.a 00 5-5 99 2828 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(5+5ζ6)q3+9ζ6q5+(2114ζ6)q7+q+(-5+5\zeta_{6})q^{3}+9\zeta_{6}q^{5}+(21-14\zeta_{6})q^{7}+\cdots
112.4.i.b 112.i 7.c 22 6.6086.608 Q(3)\Q(\sqrt{-3}) None 14.4.c.b 00 1-1 7-7 2020 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(1+ζ6)q37ζ6q5+(1+18ζ6)q7+q+(-1+\zeta_{6})q^{3}-7\zeta_{6}q^{5}+(1+18\zeta_{6})q^{7}+\cdots
112.4.i.c 112.i 7.c 22 6.6086.608 Q(3)\Q(\sqrt{-3}) None 7.4.c.a 00 77 7-7 28-28 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(77ζ6)q37ζ6q5+(714ζ6)q7+q+(7-7\zeta_{6})q^{3}-7\zeta_{6}q^{5}+(-7-14\zeta_{6})q^{7}+\cdots
112.4.i.d 112.i 7.c 44 6.6086.608 Q(3,37)\Q(\sqrt{-3}, \sqrt{37}) None 28.4.e.a 00 00 1414 24-24 SU(2)[C3]\mathrm{SU}(2)[C_{3}] qβ2q3+(77β1+2β2+2β3)q5+q-\beta _{2}q^{3}+(7-7\beta _{1}+2\beta _{2}+2\beta _{3})q^{5}+\cdots
112.4.i.e 112.i 7.c 66 6.6086.608 6.0.11163123.4 None 56.4.i.b 00 7-7 33 44 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(2β1+β5)q3+(1β1β2β3+)q5+q+(-2\beta _{1}+\beta _{5})q^{3}+(1-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots
112.4.i.f 112.i 7.c 66 6.6086.608 6.0.11163123.4 None 56.4.i.a 00 11 13-13 2020 SU(2)[C3]\mathrm{SU}(2)[C_{3}] qβ3q3+(5+5β1β3β42β5)q5+q-\beta _{3}q^{3}+(-5+5\beta _{1}-\beta _{3}-\beta _{4}-2\beta _{5})q^{5}+\cdots

Decomposition of S4old(112,[χ])S_{4}^{\mathrm{old}}(112, [\chi]) into lower level spaces

S4old(112,[χ]) S_{4}^{\mathrm{old}}(112, [\chi]) \simeq S4new(7,[χ])S_{4}^{\mathrm{new}}(7, [\chi])5^{\oplus 5}\oplusS4new(14,[χ])S_{4}^{\mathrm{new}}(14, [\chi])4^{\oplus 4}\oplusS4new(28,[χ])S_{4}^{\mathrm{new}}(28, [\chi])3^{\oplus 3}\oplusS4new(56,[χ])S_{4}^{\mathrm{new}}(56, [\chi])2^{\oplus 2}