Properties

Label 315.4.j
Level 315315
Weight 44
Character orbit 315.j
Rep. character χ315(46,)\chi_{315}(46,\cdot)
Character field Q(ζ3)\Q(\zeta_{3})
Dimension 8080
Newform subspaces 1010
Sturm bound 192192
Trace bound 55

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Defining parameters

Level: N N == 315=3257 315 = 3^{2} \cdot 5 \cdot 7
Weight: k k == 4 4
Character orbit: [χ][\chi] == 315.j (of order 33 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 7 7
Character field: Q(ζ3)\Q(\zeta_{3})
Newform subspaces: 10 10
Sturm bound: 192192
Trace bound: 55
Distinguishing TpT_p: 22, 1313

Dimensions

The following table gives the dimensions of various subspaces of M4(315,[χ])M_{4}(315, [\chi]).

Total New Old
Modular forms 304 80 224
Cusp forms 272 80 192
Eisenstein series 32 0 32

Trace form

80q+2q2170q410q5+20q7+36q8+20q1038q11352q13206q14718q16140q17154q19+200q20368q2280q231000q25438q26+4486q98+O(q100) 80 q + 2 q^{2} - 170 q^{4} - 10 q^{5} + 20 q^{7} + 36 q^{8} + 20 q^{10} - 38 q^{11} - 352 q^{13} - 206 q^{14} - 718 q^{16} - 140 q^{17} - 154 q^{19} + 200 q^{20} - 368 q^{22} - 80 q^{23} - 1000 q^{25} - 438 q^{26}+ \cdots - 4486 q^{98}+O(q^{100}) Copy content Toggle raw display

Decomposition of S4new(315,[χ])S_{4}^{\mathrm{new}}(315, [\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}
315.4.j.a 315.j 7.c 22 18.58618.586 Q(3)\Q(\sqrt{-3}) None 105.4.i.a 33 00 5-5 28-28 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+3ζ6q2+(1+ζ6)q45ζ6q5+q+3\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-5\zeta_{6}q^{5}+\cdots
315.4.j.b 315.j 7.c 22 18.58618.586 Q(3)\Q(\sqrt{-3}) None 35.4.e.a 33 00 55 28-28 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+3ζ6q2+(1+ζ6)q4+5ζ6q5+q+3\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+5\zeta_{6}q^{5}+\cdots
315.4.j.c 315.j 7.c 44 18.58618.586 Q(2,3)\Q(\sqrt{2}, \sqrt{-3}) None 35.4.e.b 6-6 00 1010 2222 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(β1+3β2+β3)q2+(36β1+)q4+q+(\beta _{1}+3\beta _{2}+\beta _{3})q^{2}+(-3-6\beta _{1}+\cdots)q^{4}+\cdots
315.4.j.d 315.j 7.c 44 18.58618.586 Q(2,3)\Q(\sqrt{2}, \sqrt{-3}) None 105.4.i.b 4-4 00 10-10 5050 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(β1+2β2β3)q2+(2+4β1+)q4+q+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{2}+(2+4\beta _{1}+\cdots)q^{4}+\cdots
315.4.j.e 315.j 7.c 66 18.58618.586 6.0.646154928.2 None 105.4.i.c 33 00 1515 2-2 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(1β1β2β3)q2+(β1+β4+)q4+q+(1-\beta _{1}-\beta _{2}-\beta _{3})q^{2}+(-\beta _{1}+\beta _{4}+\cdots)q^{4}+\cdots
315.4.j.f 315.j 7.c 1010 18.58618.586 Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots) None 105.4.i.e 1-1 00 25-25 5656 SU(2)[C3]\mathrm{SU}(2)[C_{3}] qβ1q2+(β1β2+β34β4+β8+)q4+q-\beta _{1}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}-4\beta _{4}+\beta _{8}+\cdots)q^{4}+\cdots
315.4.j.g 315.j 7.c 1010 18.58618.586 Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots) None 35.4.e.c 11 00 25-25 62-62 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+β1q2+(7β4+7β6+β8)q4+q+\beta _{1}q^{2}+(-7-\beta _{4}+7\beta _{6}+\beta _{8})q^{4}+\cdots
315.4.j.h 315.j 7.c 1010 18.58618.586 Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots) None 105.4.i.d 33 00 2525 32-32 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(β1β4)q2+(55β4+β7+)q4+q+(-\beta _{1}-\beta _{4})q^{2}+(-5-5\beta _{4}+\beta _{7}+\cdots)q^{4}+\cdots
315.4.j.i 315.j 7.c 1616 18.58618.586 Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots) None 315.4.j.i 4-4 00 4040 2222 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(β1+β6)q2+(6β1+β4β5+)q4+q+(\beta _{1}+\beta _{6})q^{2}+(-6-\beta _{1}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots
315.4.j.j 315.j 7.c 1616 18.58618.586 Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots) None 315.4.j.i 44 00 40-40 2222 SU(2)[C3]\mathrm{SU}(2)[C_{3}] q+(β1β6)q2+(6β1+β4+)q4+q+(-\beta _{1}-\beta _{6})q^{2}+(-6-\beta _{1}+\beta _{4}+\cdots)q^{4}+\cdots

Decomposition of S4old(315,[χ])S_{4}^{\mathrm{old}}(315, [\chi]) into lower level spaces

S4old(315,[χ]) S_{4}^{\mathrm{old}}(315, [\chi]) \simeq S4new(7,[χ])S_{4}^{\mathrm{new}}(7, [\chi])6^{\oplus 6}\oplusS4new(21,[χ])S_{4}^{\mathrm{new}}(21, [\chi])4^{\oplus 4}\oplusS4new(35,[χ])S_{4}^{\mathrm{new}}(35, [\chi])3^{\oplus 3}\oplusS4new(63,[χ])S_{4}^{\mathrm{new}}(63, [\chi])2^{\oplus 2}\oplusS4new(105,[χ])S_{4}^{\mathrm{new}}(105, [\chi])2^{\oplus 2}