# Properties

 Label 207.8 Level 207 Weight 8 Dimension 8649 Nonzero newspaces 8 Sturm bound 25344 Trace bound 2

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## Defining parameters

 Level: $$N$$ = $$207 = 3^{2} \cdot 23$$ Weight: $$k$$ = $$8$$ Nonzero newspaces: $$8$$ Sturm bound: $$25344$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{8}(\Gamma_1(207))$$.

Total New Old
Modular forms 11264 8837 2427
Cusp forms 10912 8649 2263
Eisenstein series 352 188 164

## Trace form

 $$8649 q - 3 q^{2} - 92 q^{3} - 135 q^{4} + 1107 q^{5} + 2422 q^{6} - 777 q^{7} - 14517 q^{8} - 2024 q^{9} + O(q^{10})$$ $$8649 q - 3 q^{2} - 92 q^{3} - 135 q^{4} + 1107 q^{5} + 2422 q^{6} - 777 q^{7} - 14517 q^{8} - 2024 q^{9} + 17757 q^{10} + 14991 q^{11} - 16148 q^{12} - 13701 q^{13} + 31743 q^{14} + 2332 q^{15} + 114241 q^{16} - 14696 q^{17} - 85796 q^{18} - 226786 q^{19} + 6967 q^{20} + 374404 q^{21} + 776390 q^{22} + 236621 q^{23} - 431026 q^{24} - 405653 q^{25} - 1533145 q^{26} - 644588 q^{27} - 958939 q^{28} + 986224 q^{29} + 2224180 q^{30} + 1062008 q^{31} + 2886209 q^{32} + 296992 q^{33} - 3740485 q^{34} - 3197935 q^{35} - 5003666 q^{36} + 1612453 q^{37} + 2090132 q^{38} + 4114588 q^{39} - 3048265 q^{40} + 1234133 q^{41} - 1077776 q^{42} - 524573 q^{43} - 4478006 q^{44} - 5375204 q^{45} + 8046029 q^{46} + 6827626 q^{47} + 14869006 q^{48} + 1441935 q^{49} - 4225286 q^{50} - 5051420 q^{51} - 24948443 q^{52} - 8870071 q^{53} + 7241490 q^{54} - 10489253 q^{55} - 40457380 q^{56} - 8874182 q^{57} + 15010166 q^{58} + 15719909 q^{59} + 43200668 q^{60} + 42108951 q^{61} + 45632583 q^{62} + 22523394 q^{63} + 10365849 q^{64} - 17849634 q^{65} - 44627136 q^{66} - 40122855 q^{67} - 134023374 q^{68} - 30029322 q^{69} - 56584134 q^{70} - 12459864 q^{71} + 28873534 q^{72} + 39677739 q^{73} + 48962914 q^{74} + 30819638 q^{75} + 135889426 q^{76} + 96947200 q^{77} + 63091816 q^{78} + 7901759 q^{79} - 21723276 q^{80} + 2606912 q^{81} - 168930045 q^{82} - 144091238 q^{83} - 126522368 q^{84} - 2005201 q^{85} + 87992611 q^{86} - 20581460 q^{87} + 104400497 q^{88} + 66650661 q^{89} + 27323964 q^{90} + 31355786 q^{91} + 34371006 q^{92} - 54662512 q^{93} - 36465850 q^{94} - 60197616 q^{95} + 7169156 q^{96} + 45966720 q^{97} + 176455815 q^{98} + 98765308 q^{99} + O(q^{100})$$

## Decomposition of $$S_{8}^{\mathrm{new}}(\Gamma_1(207))$$

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
207.8.a $$\chi_{207}(1, \cdot)$$ 207.8.a.a 5 1
207.8.a.b 5
207.8.a.c 6
207.8.a.d 7
207.8.a.e 8
207.8.a.f 8
207.8.a.g 12
207.8.a.h 12
207.8.c $$\chi_{207}(206, \cdot)$$ 207.8.c.a 56 1
207.8.e $$\chi_{207}(70, \cdot)$$ n/a 308 2
207.8.g $$\chi_{207}(68, \cdot)$$ n/a 332 2
207.8.i $$\chi_{207}(55, \cdot)$$ n/a 690 10
207.8.k $$\chi_{207}(17, \cdot)$$ n/a 560 10
207.8.m $$\chi_{207}(4, \cdot)$$ n/a 3320 20
207.8.o $$\chi_{207}(5, \cdot)$$ n/a 3320 20

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{8}^{\mathrm{old}}(\Gamma_1(207))$$ into lower level spaces

$$S_{8}^{\mathrm{old}}(\Gamma_1(207)) \cong$$ $$S_{8}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 4}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 2}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 3}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 2}$$