Properties

 Label 1305.2.c Level $1305$ Weight $2$ Character orbit 1305.c Rep. character $\chi_{1305}(784,\cdot)$ Character field $\Q$ Dimension $70$ Newform subspaces $12$ Sturm bound $360$ Trace bound $11$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$1305 = 3^{2} \cdot 5 \cdot 29$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1305.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$12$$ Sturm bound: $$360$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$2$$, $$7$$, $$11$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1305, [\chi])$$.

Total New Old
Modular forms 188 70 118
Cusp forms 172 70 102
Eisenstein series 16 0 16

Trace form

 $$70 q - 66 q^{4} + 4 q^{5} + O(q^{10})$$ $$70 q - 66 q^{4} + 4 q^{5} - 14 q^{10} + 8 q^{11} - 8 q^{14} + 82 q^{16} + 20 q^{19} - 12 q^{20} - 12 q^{26} - 6 q^{29} - 40 q^{31} - 12 q^{34} + 4 q^{35} + 10 q^{40} + 20 q^{41} - 8 q^{44} + 56 q^{46} - 62 q^{49} + 10 q^{50} + 14 q^{55} + 8 q^{56} + 16 q^{59} - 44 q^{61} - 90 q^{64} + 10 q^{65} - 32 q^{70} - 24 q^{71} + 60 q^{74} - 84 q^{76} + 56 q^{79} + 52 q^{80} + 52 q^{85} - 4 q^{86} - 36 q^{89} + 8 q^{91} + 36 q^{94} + 12 q^{95} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(1305, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1305.2.c.a $2$ $10.420$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+2iq^{2}-2q^{4}+(2-i)q^{5}-2iq^{7}+\cdots$$
1305.2.c.b $2$ $10.420$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{2}+q^{4}+(-1-2i)q^{5}+2iq^{7}+\cdots$$
1305.2.c.c $2$ $10.420$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2q^{4}+\beta q^{5}-2\beta q^{7}-5q^{11}-2\beta q^{13}+\cdots$$
1305.2.c.d $2$ $10.420$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2q^{4}-\beta q^{5}-2\beta q^{7}+5q^{11}-2\beta q^{13}+\cdots$$
1305.2.c.e $4$ $10.420$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$0$$ $$3$$ $$0$$ $$q+\beta _{2}q^{2}-q^{4}+(1-\beta _{2}+\beta _{3})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots$$
1305.2.c.f $4$ $10.420$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots$$
1305.2.c.g $4$ $10.420$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+\zeta_{8}q^{2}+q^{4}+(1+2\zeta_{8})q^{5}+\zeta_{8}^{2}q^{7}+\cdots$$
1305.2.c.h $6$ $10.420$ 6.0.84345856.2 None $$0$$ $$0$$ $$-3$$ $$0$$ $$q+\beta _{1}q^{2}+(-3+\beta _{3}+\beta _{4})q^{4}-\beta _{3}q^{5}+\cdots$$
1305.2.c.i $10$ $10.420$ 10.0.$$\cdots$$.1 None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(\beta _{1}+\beta _{2}+\beta _{9})q^{2}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$$
1305.2.c.j $10$ $10.420$ 10.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{4}+\beta _{6})q^{2}+(-1-\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots$$
1305.2.c.k $12$ $10.420$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots$$
1305.2.c.l $12$ $10.420$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+\beta _{7}q^{5}+\beta _{3}q^{7}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(1305, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1305, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(145, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(435, [\chi])$$$$^{\oplus 2}$$