Properties

 Label 155.2 Level 155 Weight 2 Dimension 789 Nonzero newspaces 12 Newforms 25 Sturm bound 3840 Trace bound 2

Defining parameters

 Level: $$N$$ = $$155 = 5 \cdot 31$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newforms: $$25$$ Sturm bound: $$3840$$ Trace bound: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(155))$$.

Total New Old
Modular forms 1080 965 115
Cusp forms 841 789 52
Eisenstein series 239 176 63

Trace form

 $$789q$$ $$\mathstrut -\mathstrut 33q^{2}$$ $$\mathstrut -\mathstrut 34q^{3}$$ $$\mathstrut -\mathstrut 37q^{4}$$ $$\mathstrut -\mathstrut 46q^{5}$$ $$\mathstrut -\mathstrut 102q^{6}$$ $$\mathstrut -\mathstrut 38q^{7}$$ $$\mathstrut -\mathstrut 45q^{8}$$ $$\mathstrut -\mathstrut 43q^{9}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$789q$$ $$\mathstrut -\mathstrut 33q^{2}$$ $$\mathstrut -\mathstrut 34q^{3}$$ $$\mathstrut -\mathstrut 37q^{4}$$ $$\mathstrut -\mathstrut 46q^{5}$$ $$\mathstrut -\mathstrut 102q^{6}$$ $$\mathstrut -\mathstrut 38q^{7}$$ $$\mathstrut -\mathstrut 45q^{8}$$ $$\mathstrut -\mathstrut 43q^{9}$$ $$\mathstrut -\mathstrut 48q^{10}$$ $$\mathstrut -\mathstrut 102q^{11}$$ $$\mathstrut -\mathstrut 58q^{12}$$ $$\mathstrut -\mathstrut 44q^{13}$$ $$\mathstrut -\mathstrut 54q^{14}$$ $$\mathstrut -\mathstrut 49q^{15}$$ $$\mathstrut -\mathstrut 121q^{16}$$ $$\mathstrut -\mathstrut 48q^{17}$$ $$\mathstrut -\mathstrut 69q^{18}$$ $$\mathstrut -\mathstrut 50q^{19}$$ $$\mathstrut -\mathstrut 52q^{20}$$ $$\mathstrut -\mathstrut 112q^{21}$$ $$\mathstrut -\mathstrut 6q^{22}$$ $$\mathstrut -\mathstrut 24q^{23}$$ $$\mathstrut +\mathstrut 30q^{24}$$ $$\mathstrut -\mathstrut 36q^{25}$$ $$\mathstrut -\mathstrut 72q^{26}$$ $$\mathstrut +\mathstrut 20q^{27}$$ $$\mathstrut +\mathstrut 74q^{28}$$ $$\mathstrut +\mathstrut 18q^{30}$$ $$\mathstrut -\mathstrut 61q^{31}$$ $$\mathstrut +\mathstrut 57q^{32}$$ $$\mathstrut -\mathstrut 18q^{33}$$ $$\mathstrut +\mathstrut 36q^{34}$$ $$\mathstrut -\mathstrut 23q^{35}$$ $$\mathstrut -\mathstrut 21q^{36}$$ $$\mathstrut +\mathstrut 22q^{37}$$ $$\mathstrut -\mathstrut 30q^{38}$$ $$\mathstrut -\mathstrut 16q^{39}$$ $$\mathstrut -\mathstrut 102q^{41}$$ $$\mathstrut -\mathstrut 66q^{42}$$ $$\mathstrut -\mathstrut 64q^{43}$$ $$\mathstrut -\mathstrut 114q^{44}$$ $$\mathstrut -\mathstrut 58q^{45}$$ $$\mathstrut -\mathstrut 162q^{46}$$ $$\mathstrut -\mathstrut 78q^{47}$$ $$\mathstrut -\mathstrut 64q^{48}$$ $$\mathstrut -\mathstrut 27q^{49}$$ $$\mathstrut +\mathstrut 27q^{50}$$ $$\mathstrut +\mathstrut 18q^{51}$$ $$\mathstrut +\mathstrut 22q^{52}$$ $$\mathstrut -\mathstrut 24q^{53}$$ $$\mathstrut +\mathstrut 180q^{54}$$ $$\mathstrut +\mathstrut 3q^{55}$$ $$\mathstrut +\mathstrut 60q^{56}$$ $$\mathstrut +\mathstrut 70q^{57}$$ $$\mathstrut +\mathstrut 90q^{58}$$ $$\mathstrut -\mathstrut 30q^{59}$$ $$\mathstrut +\mathstrut 182q^{60}$$ $$\mathstrut +\mathstrut 58q^{61}$$ $$\mathstrut +\mathstrut 57q^{62}$$ $$\mathstrut +\mathstrut 76q^{63}$$ $$\mathstrut +\mathstrut 83q^{64}$$ $$\mathstrut +\mathstrut 31q^{65}$$ $$\mathstrut +\mathstrut 216q^{66}$$ $$\mathstrut -\mathstrut 38q^{67}$$ $$\mathstrut +\mathstrut 54q^{68}$$ $$\mathstrut +\mathstrut 54q^{69}$$ $$\mathstrut +\mathstrut 66q^{70}$$ $$\mathstrut -\mathstrut 42q^{71}$$ $$\mathstrut +\mathstrut 105q^{72}$$ $$\mathstrut -\mathstrut 44q^{73}$$ $$\mathstrut +\mathstrut 6q^{74}$$ $$\mathstrut +\mathstrut 56q^{75}$$ $$\mathstrut +\mathstrut 20q^{76}$$ $$\mathstrut +\mathstrut 24q^{77}$$ $$\mathstrut +\mathstrut 72q^{78}$$ $$\mathstrut -\mathstrut 40q^{79}$$ $$\mathstrut +\mathstrut 74q^{80}$$ $$\mathstrut -\mathstrut 91q^{81}$$ $$\mathstrut -\mathstrut 36q^{82}$$ $$\mathstrut +\mathstrut 96q^{83}$$ $$\mathstrut +\mathstrut 106q^{84}$$ $$\mathstrut -\mathstrut 3q^{85}$$ $$\mathstrut +\mathstrut 18q^{86}$$ $$\mathstrut -\mathstrut 30q^{87}$$ $$\mathstrut +\mathstrut 150q^{88}$$ $$\mathstrut +\mathstrut 30q^{89}$$ $$\mathstrut +\mathstrut 141q^{90}$$ $$\mathstrut -\mathstrut 72q^{91}$$ $$\mathstrut +\mathstrut 192q^{92}$$ $$\mathstrut +\mathstrut 86q^{93}$$ $$\mathstrut -\mathstrut 84q^{94}$$ $$\mathstrut +\mathstrut 55q^{95}$$ $$\mathstrut +\mathstrut 108q^{96}$$ $$\mathstrut +\mathstrut 2q^{97}$$ $$\mathstrut +\mathstrut 159q^{98}$$ $$\mathstrut -\mathstrut 36q^{99}$$ $$\mathstrut +\mathstrut O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(155))$$

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
155.2.a $$\chi_{155}(1, \cdot)$$ 155.2.a.a 1 1
155.2.a.b 1
155.2.a.c 1
155.2.a.d 4
155.2.a.e 4
155.2.b $$\chi_{155}(94, \cdot)$$ 155.2.b.a 4 1
155.2.b.b 10
155.2.e $$\chi_{155}(36, \cdot)$$ 155.2.e.a 2 2
155.2.e.b 2
155.2.e.c 8
155.2.e.d 8
155.2.f $$\chi_{155}(92, \cdot)$$ 155.2.f.a 12 2
155.2.f.b 16
155.2.h $$\chi_{155}(16, \cdot)$$ 155.2.h.a 24 4
155.2.h.b 24
155.2.j $$\chi_{155}(129, \cdot)$$ 155.2.j.a 28 2
155.2.n $$\chi_{155}(4, \cdot)$$ 155.2.n.a 56 4
155.2.p $$\chi_{155}(37, \cdot)$$ 155.2.p.a 4 4
155.2.p.b 4
155.2.p.c 48
155.2.q $$\chi_{155}(41, \cdot)$$ 155.2.q.a 40 8
155.2.q.b 40
155.2.r $$\chi_{155}(23, \cdot)$$ 155.2.r.a 112 8
155.2.u $$\chi_{155}(9, \cdot)$$ 155.2.u.a 112 8
155.2.x $$\chi_{155}(3, \cdot)$$ 155.2.x.a 224 16

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(155))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(155)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(31))$$$$^{\oplus 2}$$