Properties

Label 825.2.p
Level 825825
Weight 22
Character orbit 825.p
Rep. character χ825(181,)\chi_{825}(181,\cdot)
Character field Q(ζ5)\Q(\zeta_{5})
Dimension 240240
Newform subspaces 33
Sturm bound 240240
Trace bound 11

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Defining parameters

Level: N N == 825=35211 825 = 3 \cdot 5^{2} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 825.p (of order 55 and degree 44)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 275 275
Character field: Q(ζ5)\Q(\zeta_{5})
Newform subspaces: 3 3
Sturm bound: 240240
Trace bound: 11
Distinguishing TpT_p: 22

Dimensions

The following table gives the dimensions of various subspaces of M2(825,[χ])M_{2}(825, [\chi]).

Total New Old
Modular forms 496 240 256
Cusp forms 464 240 224
Eisenstein series 32 0 32

Trace form

240q60q4+6q54q6+4q7+240q92q10+6q11+4q128q13+2q1556q16+2q1714q19+4q208q21+30q2232q2312q24++6q99+O(q100) 240 q - 60 q^{4} + 6 q^{5} - 4 q^{6} + 4 q^{7} + 240 q^{9} - 2 q^{10} + 6 q^{11} + 4 q^{12} - 8 q^{13} + 2 q^{15} - 56 q^{16} + 2 q^{17} - 14 q^{19} + 4 q^{20} - 8 q^{21} + 30 q^{22} - 32 q^{23} - 12 q^{24}+ \cdots + 6 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(825,[χ])S_{2}^{\mathrm{new}}(825, [\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}
825.2.p.a 825.p 275.k 44 6.5886.588 Q(ζ10)\Q(\zeta_{10}) None 825.2.p.a 5-5 44 5-5 11 SU(2)[C5]\mathrm{SU}(2)[C_{5}] q+(2+2ζ10+ζ103)q2+q33ζ10q4+q+(-2+2\zeta_{10}+\zeta_{10}^{3})q^{2}+q^{3}-3\zeta_{10}q^{4}+\cdots
825.2.p.b 825.p 275.k 116116 6.5886.588 None 825.2.p.b 33 116116 99 3-3 SU(2)[C5]\mathrm{SU}(2)[C_{5}]
825.2.p.c 825.p 275.k 120120 6.5886.588 None 825.2.p.c 22 120-120 22 66 SU(2)[C5]\mathrm{SU}(2)[C_{5}]

Decomposition of S2old(825,[χ])S_{2}^{\mathrm{old}}(825, [\chi]) into lower level spaces

S2old(825,[χ]) S_{2}^{\mathrm{old}}(825, [\chi]) \simeq S2new(275,[χ])S_{2}^{\mathrm{new}}(275, [\chi])2^{\oplus 2}