# Properties

 Label 261.2 Level 261 Weight 2 Dimension 1869 Nonzero newspaces 12 Newform subspaces 26 Sturm bound 10080 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$261 = 3^{2} \cdot 29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newform subspaces: $$26$$ Sturm bound: $$10080$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(261))$$.

Total New Old
Modular forms 2744 2111 633
Cusp forms 2297 1869 428
Eisenstein series 447 242 205

## Trace form

 $$1869q - 42q^{2} - 56q^{3} - 42q^{4} - 42q^{5} - 56q^{6} - 42q^{7} - 42q^{8} - 56q^{9} + O(q^{10})$$ $$1869q - 42q^{2} - 56q^{3} - 42q^{4} - 42q^{5} - 56q^{6} - 42q^{7} - 42q^{8} - 56q^{9} - 126q^{10} - 42q^{11} - 56q^{12} - 42q^{13} - 42q^{14} - 56q^{15} - 42q^{16} - 42q^{17} - 56q^{18} - 126q^{19} - 63q^{20} - 56q^{21} - 70q^{22} - 56q^{23} - 56q^{24} - 70q^{25} - 77q^{26} - 56q^{27} - 196q^{28} - 70q^{29} - 112q^{30} - 70q^{31} - 98q^{32} - 56q^{33} - 77q^{34} - 70q^{35} - 56q^{36} - 140q^{37} - 70q^{38} - 56q^{39} - 63q^{40} - 42q^{41} - 56q^{42} - 42q^{43} - 56q^{44} - 56q^{45} - 196q^{46} - 70q^{47} - 56q^{48} - 98q^{49} - 140q^{50} - 56q^{51} - 154q^{52} - 105q^{53} - 56q^{54} - 238q^{55} - 56q^{56} - 56q^{57} - 210q^{58} - 112q^{59} - 56q^{60} - 98q^{61} - 140q^{62} - 56q^{63} - 252q^{64} - 105q^{65} - 56q^{66} - 98q^{67} - 140q^{68} - 56q^{69} - 70q^{70} + 56q^{71} + 112q^{72} - 77q^{73} + 196q^{74} + 84q^{75} + 294q^{76} + 168q^{77} + 168q^{78} + 42q^{79} + 546q^{80} + 168q^{81} + 42q^{82} + 126q^{83} + 280q^{84} + 210q^{85} + 420q^{86} + 84q^{87} + 420q^{88} + 168q^{89} + 224q^{90} + 126q^{91} + 462q^{92} + 56q^{93} + 126q^{94} + 294q^{95} + 336q^{96} - 7q^{97} + 224q^{98} + 84q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(261))$$

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
261.2.a $$\chi_{261}(1, \cdot)$$ 261.2.a.a 2 1
261.2.a.b 2
261.2.a.c 2
261.2.a.d 2
261.2.a.e 3
261.2.c $$\chi_{261}(28, \cdot)$$ 261.2.c.a 2 1
261.2.c.b 4
261.2.c.c 6
261.2.e $$\chi_{261}(88, \cdot)$$ 261.2.e.a 22 2
261.2.e.b 34
261.2.g $$\chi_{261}(17, \cdot)$$ 261.2.g.a 4 2
261.2.g.b 8
261.2.g.c 8
261.2.i $$\chi_{261}(115, \cdot)$$ 261.2.i.a 56 2
261.2.k $$\chi_{261}(82, \cdot)$$ 261.2.k.a 6 6
261.2.k.b 18
261.2.k.c 18
261.2.k.d 24
261.2.l $$\chi_{261}(41, \cdot)$$ 261.2.l.a 112 4
261.2.o $$\chi_{261}(64, \cdot)$$ 261.2.o.a 12 6
261.2.o.b 24
261.2.o.c 36
261.2.q $$\chi_{261}(7, \cdot)$$ 261.2.q.a 336 12
261.2.r $$\chi_{261}(8, \cdot)$$ 261.2.r.a 120 12
261.2.u $$\chi_{261}(4, \cdot)$$ 261.2.u.a 336 12
261.2.x $$\chi_{261}(2, \cdot)$$ 261.2.x.a 672 24

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(261))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(261)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(87))$$$$^{\oplus 2}$$