Properties

Label 450.2.c
Level 450450
Weight 22
Character orbit 450.c
Rep. character χ450(199,)\chi_{450}(199,\cdot)
Character field Q\Q
Dimension 88
Newform subspaces 44
Sturm bound 180180
Trace bound 1111

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Defining parameters

Level: N N == 450=23252 450 = 2 \cdot 3^{2} \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 450.c (of order 22 and degree 11)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 5 5
Character field: Q\Q
Newform subspaces: 4 4
Sturm bound: 180180
Trace bound: 1111
Distinguishing TpT_p: 77, 1111

Dimensions

The following table gives the dimensions of various subspaces of M2(450,[χ])M_{2}(450, [\chi]).

Total New Old
Modular forms 114 8 106
Cusp forms 66 8 58
Eisenstein series 48 0 48

Trace form

8q8q4+6q11+4q14+8q16+14q194q2612q29+4q3118q34+18q416q4412q464q568q618q6424q718q7414q76++24q94+O(q100) 8 q - 8 q^{4} + 6 q^{11} + 4 q^{14} + 8 q^{16} + 14 q^{19} - 4 q^{26} - 12 q^{29} + 4 q^{31} - 18 q^{34} + 18 q^{41} - 6 q^{44} - 12 q^{46} - 4 q^{56} - 8 q^{61} - 8 q^{64} - 24 q^{71} - 8 q^{74} - 14 q^{76}+ \cdots + 24 q^{94}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(450,[χ])S_{2}^{\mathrm{new}}(450, [\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}
450.2.c.a 450.c 5.b 22 3.5933.593 Q(1)\Q(\sqrt{-1}) None 90.2.a.a 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+iq2q4+2iq7iq86q11+q+i q^{2}-q^{4}+2 i q^{7}-i q^{8}-6 q^{11}+\cdots
450.2.c.b 450.c 5.b 22 3.5933.593 Q(1)\Q(\sqrt{-1}) None 30.2.a.a 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+iq2q44iq7iq82iq13+q+i q^{2}-q^{4}-4 i q^{7}-i q^{8}-2 i q^{13}+\cdots
450.2.c.c 450.c 5.b 22 3.5933.593 Q(1)\Q(\sqrt{-1}) None 50.2.a.a 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+iq2q4+2iq7iq8+3q11+q+i q^{2}-q^{4}+2 i q^{7}-i q^{8}+3 q^{11}+\cdots
450.2.c.d 450.c 5.b 22 3.5933.593 Q(1)\Q(\sqrt{-1}) None 90.2.a.a 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+iq2q42iq7iq8+6q11+q+i q^{2}-q^{4}-2 i q^{7}-i q^{8}+6 q^{11}+\cdots

Decomposition of S2old(450,[χ])S_{2}^{\mathrm{old}}(450, [\chi]) into lower level spaces