# Properties

 Label 195.3.j Level $195$ Weight $3$ Character orbit 195.j Rep. character $\chi_{195}(8,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $104$ Newform subspaces $4$ Sturm bound $84$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$195 = 3 \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 195.j (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$195$$ Character field: $$\Q(i)$$ Newform subspaces: $$4$$ Sturm bound: $$84$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(195, [\chi])$$.

Total New Old
Modular forms 120 120 0
Cusp forms 104 104 0
Eisenstein series 16 16 0

## Trace form

 $$104 q - 4 q^{3} - 192 q^{4} - 4 q^{6} + O(q^{10})$$ $$104 q - 4 q^{3} - 192 q^{4} - 4 q^{6} + 32 q^{10} + 16 q^{12} - 40 q^{13} - 4 q^{15} + 304 q^{16} - 8 q^{19} - 32 q^{21} + 48 q^{22} + 68 q^{24} + 128 q^{25} - 28 q^{27} - 32 q^{30} - 48 q^{31} - 44 q^{33} + 64 q^{34} + 44 q^{39} - 88 q^{40} - 136 q^{42} - 152 q^{43} - 36 q^{45} + 56 q^{46} - 104 q^{48} - 384 q^{49} + 312 q^{52} + 192 q^{54} - 136 q^{55} - 12 q^{57} + 200 q^{60} - 72 q^{61} - 280 q^{63} - 320 q^{64} + 24 q^{66} - 200 q^{67} - 240 q^{69} - 184 q^{70} + 120 q^{73} - 196 q^{75} - 72 q^{76} + 224 q^{78} + 256 q^{81} + 40 q^{82} + 508 q^{84} + 256 q^{85} - 152 q^{87} + 264 q^{88} - 404 q^{90} + 128 q^{91} - 296 q^{96} + 336 q^{97} + 52 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(195, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
195.3.j.a $2$ $5.313$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-6$$ $$0$$ $$0$$ $$q+iq^{2}-3q^{3}+3q^{4}+5iq^{5}-3iq^{6}+\cdots$$
195.3.j.b $2$ $5.313$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-3iq^{3}+3q^{4}-5iq^{5}-3q^{6}+\cdots$$
195.3.j.c $4$ $5.313$ $$\Q(\zeta_{8})$$ None $$0$$ $$8$$ $$0$$ $$0$$ $$q+(2\zeta_{8}+2\zeta_{8}^{3})q^{2}+(2+2\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\cdots$$
195.3.j.d $96$ $5.313$ None $$0$$ $$-6$$ $$0$$ $$0$$