Properties

Label 750.2.h
Level 750750
Weight 22
Character orbit 750.h
Rep. character χ750(49,)\chi_{750}(49,\cdot)
Character field Q(ζ10)\Q(\zeta_{10})
Dimension 5656
Newform subspaces 55
Sturm bound 300300
Trace bound 1111

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Defining parameters

Level: N N == 750=2353 750 = 2 \cdot 3 \cdot 5^{3}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 750.h (of order 1010 and degree 44)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 25 25
Character field: Q(ζ10)\Q(\zeta_{10})
Newform subspaces: 5 5
Sturm bound: 300300
Trace bound: 1111
Distinguishing TpT_p: 77

Dimensions

The following table gives the dimensions of various subspaces of M2(750,[χ])M_{2}(750, [\chi]).

Total New Old
Modular forms 680 56 624
Cusp forms 520 56 464
Eisenstein series 160 0 160

Trace form

56q+14q4+2q6+14q912q1114q16+20q17+8q19+4q21+20q22+20q23+8q24+32q26+10q288q296q31+20q33+40q3414q36+8q99+O(q100) 56 q + 14 q^{4} + 2 q^{6} + 14 q^{9} - 12 q^{11} - 14 q^{16} + 20 q^{17} + 8 q^{19} + 4 q^{21} + 20 q^{22} + 20 q^{23} + 8 q^{24} + 32 q^{26} + 10 q^{28} - 8 q^{29} - 6 q^{31} + 20 q^{33} + 40 q^{34} - 14 q^{36}+ \cdots - 8 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(750,[χ])S_{2}^{\mathrm{new}}(750, [\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}
750.2.h.a 750.h 25.e 88 5.9895.989 Q(ζ20)\Q(\zeta_{20}) None 150.2.g.b 00 00 00 00 SU(2)[C10]\mathrm{SU}(2)[C_{10}] q+ζ20q2+ζ207q3+ζ202q4+(1+)q6+q+\zeta_{20}q^{2}+\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+(-1+\cdots)q^{6}+\cdots
750.2.h.b 750.h 25.e 88 5.9895.989 Q(ζ20)\Q(\zeta_{20}) None 150.2.g.a 00 00 00 00 SU(2)[C10]\mathrm{SU}(2)[C_{10}] q+ζ20q2ζ207q3+ζ202q4+(1+)q6+q+\zeta_{20}q^{2}-\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+(1+\cdots)q^{6}+\cdots
750.2.h.c 750.h 25.e 88 5.9895.989 Q(ζ20)\Q(\zeta_{20}) None 150.2.h.a 00 00 00 00 SU(2)[C10]\mathrm{SU}(2)[C_{10}] q+ζ20q2ζ207q3+ζ202q4+(1+)q6+q+\zeta_{20}q^{2}-\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+(1+\cdots)q^{6}+\cdots
750.2.h.d 750.h 25.e 1616 5.9895.989 Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots) None 150.2.h.b 00 00 00 00 SU(2)[C10]\mathrm{SU}(2)[C_{10}] q+β6q2+β3q3+β8q4+β2q6+q+\beta _{6}q^{2}+\beta _{3}q^{3}+\beta _{8}q^{4}+\beta _{2}q^{6}+\cdots
750.2.h.e 750.h 25.e 1616 5.9895.989 16.0.\cdots.12 None 150.2.g.c 00 00 00 00 SU(2)[C10]\mathrm{SU}(2)[C_{10}] q+β11q2+β7q3+β9q4+(1+β1+)q6+q+\beta _{11}q^{2}+\beta _{7}q^{3}+\beta _{9}q^{4}+(1+\beta _{1}+\cdots)q^{6}+\cdots

Decomposition of S2old(750,[χ])S_{2}^{\mathrm{old}}(750, [\chi]) into lower level spaces