Properties

Label 605.2.m
Level 605605
Weight 22
Character orbit 605.m
Rep. character χ605(112,)\chi_{605}(112,\cdot)
Character field Q(ζ20)\Q(\zeta_{20})
Dimension 368368
Newform subspaces 77
Sturm bound 132132
Trace bound 77

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Defining parameters

Level: N N == 605=5112 605 = 5 \cdot 11^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 605.m (of order 2020 and degree 88)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 55 55
Character field: Q(ζ20)\Q(\zeta_{20})
Newform subspaces: 7 7
Sturm bound: 132132
Trace bound: 77
Distinguishing TpT_p: 22

Dimensions

The following table gives the dimensions of various subspaces of M2(605,[χ])M_{2}(605, [\chi]).

Total New Old
Modular forms 624 496 128
Cusp forms 432 368 64
Eisenstein series 192 128 64

Trace form

368q+10q2+2q3+2q5+20q6+10q8124q12+10q1322q15+40q16+10q1824q2064q2310q2528q26+14q2750q2830q30++14q97+O(q100) 368 q + 10 q^{2} + 2 q^{3} + 2 q^{5} + 20 q^{6} + 10 q^{8} - 124 q^{12} + 10 q^{13} - 22 q^{15} + 40 q^{16} + 10 q^{18} - 24 q^{20} - 64 q^{23} - 10 q^{25} - 28 q^{26} + 14 q^{27} - 50 q^{28} - 30 q^{30}+ \cdots + 14 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(605,[χ])S_{2}^{\mathrm{new}}(605, [\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}
605.2.m.a 605.m 55.l 1616 4.8314.831 16.0.\cdots.1 Q(11)\Q(\sqrt{-11}) 55.2.e.b 00 22 00 00 U(1)[D20]\mathrm{U}(1)[D_{20}] q+(β1+β4+β5)q3+(2β52β7+)q4+q+(\beta _{1}+\beta _{4}+\beta _{5})q^{3}+(-2\beta _{5}-2\beta _{7}+\cdots)q^{4}+\cdots
605.2.m.b 605.m 55.l 1616 4.8314.831 Q(ζ40)\Q(\zeta_{40}) None 55.2.e.a 00 44 88 00 SU(2)[C20]\mathrm{SU}(2)[C_{20}] q+(β15+β12++β9)q2++(β6+β1)q3+q+(\beta_{15}+\beta_{12}+\cdots+\beta_{9})q^{2}+\cdots+(\beta_{6}+\beta_1)q^{3}+\cdots
605.2.m.c 605.m 55.l 3232 4.8314.831 None 55.2.l.a 00 66 2-2 20-20 SU(2)[C20]\mathrm{SU}(2)[C_{20}]
605.2.m.d 605.m 55.l 3232 4.8314.831 None 55.2.l.a 00 66 2-2 2020 SU(2)[C20]\mathrm{SU}(2)[C_{20}]
605.2.m.e 605.m 55.l 3232 4.8314.831 None 55.2.l.a 1010 4-4 2-2 00 SU(2)[C20]\mathrm{SU}(2)[C_{20}]
605.2.m.f 605.m 55.l 8080 4.8314.831 None 605.2.e.a 00 4-4 4-4 00 SU(2)[C20]\mathrm{SU}(2)[C_{20}]
605.2.m.g 605.m 55.l 160160 4.8314.831 None 605.2.e.c 00 8-8 44 00 SU(2)[C20]\mathrm{SU}(2)[C_{20}]

Decomposition of S2old(605,[χ])S_{2}^{\mathrm{old}}(605, [\chi]) into lower level spaces

S2old(605,[χ]) S_{2}^{\mathrm{old}}(605, [\chi]) \simeq S2new(55,[χ])S_{2}^{\mathrm{new}}(55, [\chi])2^{\oplus 2}