Properties

Label 1200.2.f
Level 12001200
Weight 22
Character orbit 1200.f
Rep. character χ1200(49,)\chi_{1200}(49,\cdot)
Character field Q\Q
Dimension 1818
Newform subspaces 99
Sturm bound 480480
Trace bound 1919

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Defining parameters

Level: N N == 1200=24352 1200 = 2^{4} \cdot 3 \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1200.f (of order 22 and degree 11)
Character conductor: cond(χ)\operatorname{cond}(\chi) == 5 5
Character field: Q\Q
Newform subspaces: 9 9
Sturm bound: 480480
Trace bound: 1919
Distinguishing TpT_p: 77, 1111, 1313

Dimensions

The following table gives the dimensions of various subspaces of M2(1200,[χ])M_{2}(1200, [\chi]).

Total New Old
Modular forms 276 18 258
Cusp forms 204 18 186
Eisenstein series 72 0 72

Trace form

18q18q920q19+4q294q31+8q39+20q4126q49+20q5132q5920q61+16q69+32q71+18q8136q89+68q91+O(q100) 18 q - 18 q^{9} - 20 q^{19} + 4 q^{29} - 4 q^{31} + 8 q^{39} + 20 q^{41} - 26 q^{49} + 20 q^{51} - 32 q^{59} - 20 q^{61} + 16 q^{69} + 32 q^{71} + 18 q^{81} - 36 q^{89} + 68 q^{91}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(1200,[χ])S_{2}^{\mathrm{new}}(1200, [\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}
1200.2.f.a 1200.f 5.b 22 9.5829.582 Q(1)\Q(\sqrt{-1}) None 300.2.a.b 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+iq3+iq7q96q115iq13+q+i q^{3}+i q^{7}-q^{9}-6 q^{11}-5 i q^{13}+\cdots
1200.2.f.b 1200.f 5.b 22 9.5829.582 Q(1)\Q(\sqrt{-1}) None 24.2.a.a 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qiq3q94q11+2iq13+2iq17+q-i q^{3}-q^{9}-4 q^{11}+2 i q^{13}+2 i q^{17}+\cdots
1200.2.f.c 1200.f 5.b 22 9.5829.582 Q(1)\Q(\sqrt{-1}) None 600.2.a.b 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qiq3+3iq7q92q113iq13+q-i q^{3}+3 i q^{7}-q^{9}-2 q^{11}-3 i q^{13}+\cdots
1200.2.f.d 1200.f 5.b 22 9.5829.582 Q(1)\Q(\sqrt{-1}) None 75.2.a.a 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qiq3+3iq7q92q11iq13+q-i q^{3}+3 i q^{7}-q^{9}-2 q^{11}-i q^{13}+\cdots
1200.2.f.e 1200.f 5.b 22 9.5829.582 Q(1)\Q(\sqrt{-1}) None 30.2.a.a 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+iq3+4iq7q92iq13+q+i q^{3}+4 i q^{7}-q^{9}-2 i q^{13}+\cdots
1200.2.f.f 1200.f 5.b 22 9.5829.582 Q(1)\Q(\sqrt{-1}) None 120.2.a.a 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] qiq3+4iq7q96iq13+q-i q^{3}+4 i q^{7}-q^{9}-6 i q^{13}+\cdots
1200.2.f.g 1200.f 5.b 22 9.5829.582 Q(1)\Q(\sqrt{-1}) None 120.2.a.b 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+iq3q9+4q116iq136iq17+q+i q^{3}-q^{9}+4 q^{11}-6 i q^{13}-6 i q^{17}+\cdots
1200.2.f.h 1200.f 5.b 22 9.5829.582 Q(1)\Q(\sqrt{-1}) None 15.2.a.a 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+iq3q9+4q112iq132iq17+q+i q^{3}-q^{9}+4 q^{11}-2 i q^{13}-2 i q^{17}+\cdots
1200.2.f.i 1200.f 5.b 22 9.5829.582 Q(1)\Q(\sqrt{-1}) None 600.2.a.e 00 00 00 00 SU(2)[C2]\mathrm{SU}(2)[C_{2}] q+iq3+5iq7q9+6q11+3iq13+q+i q^{3}+5 i q^{7}-q^{9}+6 q^{11}+3 i q^{13}+\cdots

Decomposition of S2old(1200,[χ])S_{2}^{\mathrm{old}}(1200, [\chi]) into lower level spaces