Properties

Label 1078.2.e
Level 10781078
Weight 22
Character orbit 1078.e
Rep. character χ1078(67,)\chi_{1078}(67,\cdot)
Character field Q(ζ3)\Q(\zeta_{3})
Dimension 6464
Newform subspaces 2222
Sturm bound 336336
Trace bound 2323

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Defining parameters

Level: N N == 1078=27211 1078 = 2 \cdot 7^{2} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1078.e (of order 33 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 7 7
Character field: Q(ζ3)\Q(\zeta_{3})
Newform subspaces: 22 22
Sturm bound: 336336
Trace bound: 2323
Distinguishing TpT_p: 33, 55, 1313

Dimensions

The following table gives the dimensions of various subspaces of M2(1078,[χ])M_{2}(1078, [\chi]).

Total New Old
Modular forms 368 64 304
Cusp forms 304 64 240
Eisenstein series 64 0 64

Trace form

64q32q44q58q624q98q13+8q1532q16+12q1716q18+8q2032q23+4q2440q2512q26+24q27+8q294q314q33++96q97+O(q100) 64 q - 32 q^{4} - 4 q^{5} - 8 q^{6} - 24 q^{9} - 8 q^{13} + 8 q^{15} - 32 q^{16} + 12 q^{17} - 16 q^{18} + 8 q^{20} - 32 q^{23} + 4 q^{24} - 40 q^{25} - 12 q^{26} + 24 q^{27} + 8 q^{29} - 4 q^{31} - 4 q^{33}+ \cdots + 96 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(1078,[χ])S_{2}^{\mathrm{new}}(1078, [\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}
1078.2.e.a 1078.e 7.c 22 8.6088.608 Q(3)\Q(\sqrt{-3}) None 1078.2.a.h 1-1 2-2 2-2 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] qζ6q2+(2+2ζ6)q3+(1+ζ6)q4+q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots
1078.2.e.b 1078.e 7.c 22 8.6088.608 Q(3)\Q(\sqrt{-3}) None 154.2.a.c 1-1 00 2-2 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] qζ6q2+(1+ζ6)q42ζ6q5+q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots
1078.2.e.c 1078.e 7.c 22 8.6088.608 Q(3)\Q(\sqrt{-3}) None 154.2.a.c 1-1 00 22 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] qζ6q2+(1+ζ6)q4+2ζ6q5+q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots
1078.2.e.d 1078.e 7.c 22 8.6088.608 Q(3)\Q(\sqrt{-3}) None 154.2.e.b 1-1 11 00 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] qζ6q2+(1ζ6)q3+(1+ζ6)q4+q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots
1078.2.e.e 1078.e 7.c 22 8.6088.608 Q(3)\Q(\sqrt{-3}) None 1078.2.a.h 1-1 22 22 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] qζ6q2+(22ζ6)q3+(1+ζ6)q4+q-\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots
1078.2.e.f 1078.e 7.c 22 8.6088.608 Q(3)\Q(\sqrt{-3}) None 154.2.e.a 1-1 33 22 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] qζ6q2+(33ζ6)q3+(1+ζ6)q4+q-\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots
1078.2.e.g 1078.e 7.c 22 8.6088.608 Q(3)\Q(\sqrt{-3}) None 154.2.e.d 11 3-3 4-4 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+ζ6q2+(3+3ζ6)q3+(1+ζ6)q4+q+\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots
1078.2.e.h 1078.e 7.c 22 8.6088.608 Q(3)\Q(\sqrt{-3}) None 154.2.a.b 11 2-2 2-2 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+ζ6q2+(2+2ζ6)q3+(1+ζ6)q4+q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots
1078.2.e.i 1078.e 7.c 22 8.6088.608 Q(3)\Q(\sqrt{-3}) None 154.2.a.a 11 00 4-4 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+ζ6q2+(1+ζ6)q44ζ6q5+q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-4\zeta_{6}q^{5}+\cdots
1078.2.e.j 1078.e 7.c 22 8.6088.608 Q(3)\Q(\sqrt{-3}) None 154.2.a.a 11 00 44 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+ζ6q2+(1+ζ6)q4+4ζ6q5+q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+4\zeta_{6}q^{5}+\cdots
1078.2.e.k 1078.e 7.c 22 8.6088.608 Q(3)\Q(\sqrt{-3}) None 154.2.e.c 11 11 00 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+ζ6q2+(1ζ6)q3+(1+ζ6)q4+q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots
1078.2.e.l 1078.e 7.c 22 8.6088.608 Q(3)\Q(\sqrt{-3}) None 154.2.a.b 11 22 22 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+ζ6q2+(22ζ6)q3+(1+ζ6)q4+q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots
1078.2.e.m 1078.e 7.c 44 8.6088.608 Q(2,3)\Q(\sqrt{2}, \sqrt{-3}) None 154.2.e.e 2-2 2-2 4-4 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+β2q2+(1+β1β2)q3+(1+)q4+q+\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots
1078.2.e.n 1078.e 7.c 44 8.6088.608 Q(3,5)\Q(\sqrt{-3}, \sqrt{5}) None 154.2.a.d 2-2 2-2 22 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+β1q2+(1β1β2)q3+(1+)q4+q+\beta _{1}q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots
1078.2.e.o 1078.e 7.c 44 8.6088.608 Q(2,3)\Q(\sqrt{2}, \sqrt{-3}) None 1078.2.a.v 2-2 00 00 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+β2q2+2β1q3+(1β2)q4+q+\beta _{2}q^{2}+2\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\cdots
1078.2.e.p 1078.e 7.c 44 8.6088.608 Q(2,3)\Q(\sqrt{2}, \sqrt{-3}) None 1078.2.a.u 2-2 00 00 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+β2q2+β1q3+(1β2)q4+(3β1+)q5+q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(-3\beta _{1}+\cdots)q^{5}+\cdots
1078.2.e.q 1078.e 7.c 44 8.6088.608 Q(3,5)\Q(\sqrt{-3}, \sqrt{5}) None 154.2.a.d 2-2 22 2-2 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+β1q2+(1+β1+β2)q3+(1β1+)q4+q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots
1078.2.e.r 1078.e 7.c 44 8.6088.608 Q(2,3)\Q(\sqrt{2}, \sqrt{-3}) None 1078.2.a.r 22 00 00 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] qβ2q2+β1q3+(1β2)q4β3q6+q-\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}-\beta _{3}q^{6}+\cdots
1078.2.e.s 1078.e 7.c 44 8.6088.608 Q(2,3)\Q(\sqrt{2}, \sqrt{-3}) None 1078.2.a.q 22 00 00 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] qβ2q2+β1q3+(1β2)q4+(β1+)q5+q-\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots
1078.2.e.t 1078.e 7.c 44 8.6088.608 Q(2,3)\Q(\sqrt{2}, \sqrt{-3}) None 1078.2.a.p 22 00 00 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(1+β2)q2+β2q42β1q5q8+q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}-2\beta _{1}q^{5}-q^{8}+\cdots
1078.2.e.u 1078.e 7.c 44 8.6088.608 Q(2,3)\Q(\sqrt{2}, \sqrt{-3}) None 1078.2.a.o 22 00 00 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(1+β2)q2+β2q4β1q5q8+q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}-\beta _{1}q^{5}-q^{8}+\cdots
1078.2.e.v 1078.e 7.c 44 8.6088.608 Q(3,7)\Q(\sqrt{-3}, \sqrt{7}) None 154.2.e.f 22 00 22 00 SU(2)[C3]\mathrm{SU}(2)[C_{3}] qβ2q2+β1q3+(1β2)q4+(β1+)q5+q-\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots

Decomposition of S2old(1078,[χ])S_{2}^{\mathrm{old}}(1078, [\chi]) into lower level spaces

S2old(1078,[χ]) S_{2}^{\mathrm{old}}(1078, [\chi]) \simeq S2new(49,[χ])S_{2}^{\mathrm{new}}(49, [\chi])4^{\oplus 4}\oplusS2new(77,[χ])S_{2}^{\mathrm{new}}(77, [\chi])4^{\oplus 4}\oplusS2new(98,[χ])S_{2}^{\mathrm{new}}(98, [\chi])2^{\oplus 2}\oplusS2new(154,[χ])S_{2}^{\mathrm{new}}(154, [\chi])2^{\oplus 2}\oplusS2new(539,[χ])S_{2}^{\mathrm{new}}(539, [\chi])2^{\oplus 2}