# Properties

 Label 195.2.bb Level $195$ Weight $2$ Character orbit 195.bb Rep. character $\chi_{195}(121,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $20$ Newform subspaces $3$ Sturm bound $56$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$195 = 3 \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 195.bb (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ Sturm bound: $$56$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(195, [\chi])$$.

Total New Old
Modular forms 64 20 44
Cusp forms 48 20 28
Eisenstein series 16 0 16

## Trace form

 $$20 q - 2 q^{3} + 12 q^{4} + 6 q^{7} - 10 q^{9} + O(q^{10})$$ $$20 q - 2 q^{3} + 12 q^{4} + 6 q^{7} - 10 q^{9} + 4 q^{10} - 8 q^{12} - 2 q^{13} - 8 q^{14} - 8 q^{16} - 12 q^{17} - 12 q^{19} - 24 q^{20} + 12 q^{22} - 4 q^{23} - 20 q^{25} - 32 q^{26} + 4 q^{27} - 12 q^{28} + 8 q^{29} + 4 q^{30} + 60 q^{32} - 4 q^{35} + 12 q^{36} - 12 q^{37} - 4 q^{39} + 24 q^{40} - 20 q^{42} + 18 q^{43} + 72 q^{46} - 24 q^{48} + 24 q^{51} + 36 q^{52} - 32 q^{53} - 8 q^{55} + 16 q^{56} - 24 q^{58} + 30 q^{61} - 52 q^{62} - 6 q^{63} - 16 q^{64} + 20 q^{65} - 24 q^{66} - 30 q^{67} + 24 q^{68} - 4 q^{69} + 48 q^{71} - 4 q^{74} + 2 q^{75} - 48 q^{76} + 40 q^{77} - 8 q^{78} + 20 q^{79} - 10 q^{81} - 16 q^{82} + 36 q^{84} - 16 q^{87} + 8 q^{88} + 24 q^{89} - 8 q^{90} - 26 q^{91} + 8 q^{92} - 6 q^{93} + 24 q^{94} - 8 q^{95} - 18 q^{97} - 96 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(195, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
195.2.bb.a $4$ $1.557$ $$\Q(\zeta_{12})$$ None $$-6$$ $$-2$$ $$0$$ $$-12$$ $$q+(-1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}^{2}+\cdots)q^{3}+\cdots$$
195.2.bb.b $8$ $1.557$ 8.0.191102976.5 None $$0$$ $$4$$ $$0$$ $$12$$ $$q+(2\beta _{1}+\beta _{3}-\beta _{5}-\beta _{7})q^{2}+(1-\beta _{4}+\cdots)q^{3}+\cdots$$
195.2.bb.c $8$ $1.557$ 8.0.56070144.2 None $$6$$ $$-4$$ $$0$$ $$6$$ $$q+(1-\beta _{1}-\beta _{2}-\beta _{4}+\beta _{5}+\beta _{6})q^{2}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(195, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(195, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 2}$$