Properties

Label 225.4.m
Level 225225
Weight 44
Character orbit 225.m
Rep. character χ225(19,)\chi_{225}(19,\cdot)
Character field Q(ζ10)\Q(\zeta_{10})
Dimension 144144
Newform subspaces 33
Sturm bound 120120
Trace bound 11

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Defining parameters

Level: N N == 225=3252 225 = 3^{2} \cdot 5^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 225.m (of order 1010 and degree 44)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 25 25
Character field: Q(ζ10)\Q(\zeta_{10})
Newform subspaces: 3 3
Sturm bound: 120120
Trace bound: 11
Distinguishing TpT_p: 22

Dimensions

The following table gives the dimensions of various subspaces of M4(225,[χ])M_{4}(225, [\chi]).

Total New Old
Modular forms 376 152 224
Cusp forms 344 144 200
Eisenstein series 32 8 24

Trace form

144q+5q2+133q49q5100q8+31q10+q115q13+101q14607q16155q1743q19+9q20690q22+85q23+109q25+474q2645q28++1840q98+O(q100) 144 q + 5 q^{2} + 133 q^{4} - 9 q^{5} - 100 q^{8} + 31 q^{10} + q^{11} - 5 q^{13} + 101 q^{14} - 607 q^{16} - 155 q^{17} - 43 q^{19} + 9 q^{20} - 690 q^{22} + 85 q^{23} + 109 q^{25} + 474 q^{26} - 45 q^{28}+ \cdots + 1840 q^{98}+O(q^{100}) Copy content Toggle raw display

Decomposition of S4new(225,[χ])S_{4}^{\mathrm{new}}(225, [\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}
225.4.m.a 225.m 25.e 2424 13.27513.275 None 25.4.e.a 55 00 15-15 00 SU(2)[C10]\mathrm{SU}(2)[C_{10}]
225.4.m.b 225.m 25.e 5656 13.27513.275 None 225.4.m.b 00 00 00 00 SU(2)[C10]\mathrm{SU}(2)[C_{10}]
225.4.m.c 225.m 25.e 6464 13.27513.275 None 75.4.i.a 00 00 66 00 SU(2)[C10]\mathrm{SU}(2)[C_{10}]

Decomposition of S4old(225,[χ])S_{4}^{\mathrm{old}}(225, [\chi]) into lower level spaces

S4old(225,[χ]) S_{4}^{\mathrm{old}}(225, [\chi]) \simeq S4new(25,[χ])S_{4}^{\mathrm{new}}(25, [\chi])3^{\oplus 3}\oplusS4new(75,[χ])S_{4}^{\mathrm{new}}(75, [\chi])2^{\oplus 2}