Properties

Label 750.2.m
Level 750750
Weight 22
Character orbit 750.m
Rep. character χ750(31,)\chi_{750}(31,\cdot)
Character field Q(ζ25)\Q(\zeta_{25})
Dimension 480480
Newform subspaces 44
Sturm bound 300300
Trace bound 1010

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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.m (of order 2525 and degree 2020)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 125 125
Character field: Q(ζ25)\Q(\zeta_{25})
Newform subspaces: 4 4
Sturm bound: 300300
Trace bound: 1010
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 3080 480 2600
Cusp forms 2920 480 2440
Eisenstein series 160 0 160

Trace form

480q+20q11+20q17+10q18+20q19+10q20+20q2240q23+10q2480q25+10q28+40q29+20q30+10q31+10q32+20q33+30q34+20q35++80q98+O(q100) 480 q + 20 q^{11} + 20 q^{17} + 10 q^{18} + 20 q^{19} + 10 q^{20} + 20 q^{22} - 40 q^{23} + 10 q^{24} - 80 q^{25} + 10 q^{28} + 40 q^{29} + 20 q^{30} + 10 q^{31} + 10 q^{32} + 20 q^{33} + 30 q^{34} + 20 q^{35}+ \cdots + 80 q^{98}+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.m.a 750.m 125.g 100100 5.9895.989 None 750.2.m.a 00 00 20-20 55 SU(2)[C25]\mathrm{SU}(2)[C_{25}]
750.2.m.b 750.m 125.g 120120 5.9895.989 None 750.2.m.b 00 00 2020 5-5 SU(2)[C25]\mathrm{SU}(2)[C_{25}]
750.2.m.c 750.m 125.g 120120 5.9895.989 None 750.2.m.c 00 00 2020 5-5 SU(2)[C25]\mathrm{SU}(2)[C_{25}]
750.2.m.d 750.m 125.g 140140 5.9895.989 None 750.2.m.d 00 00 20-20 55 SU(2)[C25]\mathrm{SU}(2)[C_{25}]

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

S2old(750,[χ]) S_{2}^{\mathrm{old}}(750, [\chi]) \simeq S2new(125,[χ])S_{2}^{\mathrm{new}}(125, [\chi])4^{\oplus 4}\oplusS2new(250,[χ])S_{2}^{\mathrm{new}}(250, [\chi])2^{\oplus 2}\oplusS2new(375,[χ])S_{2}^{\mathrm{new}}(375, [\chi])2^{\oplus 2}