Properties

Label 2400.2.w
Level 24002400
Weight 22
Character orbit 2400.w
Rep. character χ2400(607,)\chi_{2400}(607,\cdot)
Character field Q(ζ4)\Q(\zeta_{4})
Dimension 7272
Newform subspaces 1212
Sturm bound 960960
Trace bound 1717

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Defining parameters

Level: N N == 2400=25352 2400 = 2^{5} \cdot 3 \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2400.w (of order 44 and degree 22)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 20 20
Character field: Q(i)\Q(i)
Newform subspaces: 12 12
Sturm bound: 960960
Trace bound: 1717
Distinguishing TpT_p: 77, 1717

Dimensions

The following table gives the dimensions of various subspaces of M2(2400,[χ])M_{2}(2400, [\chi]).

Total New Old
Modular forms 1056 72 984
Cusp forms 864 72 792
Eisenstein series 192 0 192

Trace form

72q+8q1324q1716q338q3764q418q53+40q73+96q7772q81+32q9324q97+O(q100) 72 q + 8 q^{13} - 24 q^{17} - 16 q^{33} - 8 q^{37} - 64 q^{41} - 8 q^{53} + 40 q^{73} + 96 q^{77} - 72 q^{81} + 32 q^{93} - 24 q^{97}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(2400,[χ])S_{2}^{\mathrm{new}}(2400, [\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}
2400.2.w.a 2400.w 20.e 44 19.16419.164 Q(ζ8)\Q(\zeta_{8}) None 2400.2.w.a 00 00 00 8-8 SU(2)[C4]\mathrm{SU}(2)[C_{4}] qζ8q3+(2+2ζ822ζ83)q7+q-\zeta_{8}q^{3}+(-2+2\zeta_{8}^{2}-2\zeta_{8}^{3})q^{7}+\cdots
2400.2.w.b 2400.w 20.e 44 19.16419.164 Q(ζ8)\Q(\zeta_{8}) None 2400.2.w.a 00 00 00 8-8 SU(2)[C4]\mathrm{SU}(2)[C_{4}] qζ8q3+(2+2ζ822ζ83)q7+q-\zeta_{8}q^{3}+(-2+2\zeta_{8}^{2}-2\zeta_{8}^{3})q^{7}+\cdots
2400.2.w.c 2400.w 20.e 44 19.16419.164 Q(ζ8)\Q(\zeta_{8}) None 480.2.w.a 00 00 00 4-4 SU(2)[C4]\mathrm{SU}(2)[C_{4}] qζ8q3+(1+ζ82)q7+ζ82q9+q-\zeta_{8}q^{3}+(-1+\zeta_{8}^{2})q^{7}+\zeta_{8}^{2}q^{9}+\cdots
2400.2.w.d 2400.w 20.e 44 19.16419.164 Q(ζ8)\Q(\zeta_{8}) None 480.2.w.a 00 00 00 44 SU(2)[C4]\mathrm{SU}(2)[C_{4}] qζ8q3+(1ζ82)q7+ζ82q9+(ζ8+)q11+q-\zeta_{8}q^{3}+(1-\zeta_{8}^{2})q^{7}+\zeta_{8}^{2}q^{9}+(-\zeta_{8}+\cdots)q^{11}+\cdots
2400.2.w.e 2400.w 20.e 44 19.16419.164 Q(ζ8)\Q(\zeta_{8}) None 2400.2.w.a 00 00 00 88 SU(2)[C4]\mathrm{SU}(2)[C_{4}] qζ8q3+(22ζ822ζ83)q7+ζ82q9+q-\zeta_{8}q^{3}+(2-2\zeta_{8}^{2}-2\zeta_{8}^{3})q^{7}+\zeta_{8}^{2}q^{9}+\cdots
2400.2.w.f 2400.w 20.e 44 19.16419.164 Q(ζ8)\Q(\zeta_{8}) None 2400.2.w.a 00 00 00 88 SU(2)[C4]\mathrm{SU}(2)[C_{4}] qζ8q3+(22ζ822ζ83)q7+ζ82q9+q-\zeta_{8}q^{3}+(2-2\zeta_{8}^{2}-2\zeta_{8}^{3})q^{7}+\zeta_{8}^{2}q^{9}+\cdots
2400.2.w.g 2400.w 20.e 88 19.16419.164 Q(ζ24)\Q(\zeta_{24}) None 2400.2.w.g 00 00 00 8-8 SU(2)[C4]\mathrm{SU}(2)[C_{4}] qβ1q3+(β6β5β4+1)q7+q-\beta_1 q^{3}+(\beta_{6}-\beta_{5}-\beta_{4}+\cdots-1)q^{7}+\cdots
2400.2.w.h 2400.w 20.e 88 19.16419.164 Q(ζ24)\Q(\zeta_{24}) None 2400.2.w.g 00 00 00 8-8 SU(2)[C4]\mathrm{SU}(2)[C_{4}] qβ1q3+(β6β5β4+1)q7+q-\beta_1 q^{3}+(\beta_{6}-\beta_{5}-\beta_{4}+\cdots-1)q^{7}+\cdots
2400.2.w.i 2400.w 20.e 88 19.16419.164 8.0.1698758656.6 None 480.2.w.c 00 00 00 4-4 SU(2)[C4]\mathrm{SU}(2)[C_{4}] qβ2q3+(1β4β6)q7β4q9+q-\beta _{2}q^{3}+(-1-\beta _{4}-\beta _{6})q^{7}-\beta _{4}q^{9}+\cdots
2400.2.w.j 2400.w 20.e 88 19.16419.164 8.0.1698758656.6 None 480.2.w.c 00 00 00 44 SU(2)[C4]\mathrm{SU}(2)[C_{4}] q+β3q3+(1+β5)q7+β4q9+(β1+)q11+q+\beta _{3}q^{3}+(1+\beta _{5})q^{7}+\beta _{4}q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots
2400.2.w.k 2400.w 20.e 88 19.16419.164 Q(ζ24)\Q(\zeta_{24}) None 2400.2.w.g 00 00 00 88 SU(2)[C4]\mathrm{SU}(2)[C_{4}] qβ1q3+(β6β5+β4++1)q7+q-\beta_1 q^{3}+(-\beta_{6}-\beta_{5}+\beta_{4}+\cdots+1)q^{7}+\cdots
2400.2.w.l 2400.w 20.e 88 19.16419.164 Q(ζ24)\Q(\zeta_{24}) None 2400.2.w.g 00 00 00 88 SU(2)[C4]\mathrm{SU}(2)[C_{4}] qβ1q3+(β6β5+β4++1)q7+q-\beta_1 q^{3}+(-\beta_{6}-\beta_{5}+\beta_{4}+\cdots+1)q^{7}+\cdots

Decomposition of S2old(2400,[χ])S_{2}^{\mathrm{old}}(2400, [\chi]) into lower level spaces