Properties

 Label 2704.2.f Level $2704$ Weight $2$ Character orbit 2704.f Rep. character $\chi_{2704}(337,\cdot)$ Character field $\Q$ Dimension $72$ Newform subspaces $18$ Sturm bound $728$ Trace bound $23$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$2704 = 2^{4} \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2704.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$18$$ Sturm bound: $$728$$ Trace bound: $$23$$ Distinguishing $$T_p$$: $$3$$, $$5$$, $$11$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2704, [\chi])$$.

Total New Old
Modular forms 406 82 324
Cusp forms 322 72 250
Eisenstein series 84 10 74

Trace form

 $$72 q - 4 q^{3} + 64 q^{9} + O(q^{10})$$ $$72 q - 4 q^{3} + 64 q^{9} - 8 q^{23} - 48 q^{25} + 8 q^{27} + 4 q^{29} - 4 q^{35} + 36 q^{43} - 24 q^{49} - 20 q^{51} - 20 q^{53} + 24 q^{55} - 16 q^{61} + 24 q^{69} + 32 q^{75} - 20 q^{77} + 4 q^{79} + 56 q^{81} + 4 q^{87} - 52 q^{95} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(2704, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2704.2.f.a $2$ $21.592$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-6$$ $$0$$ $$0$$ $$q-3q^{3}+2iq^{5}+iq^{7}+6q^{9}-5iq^{11}+\cdots$$
2704.2.f.b $2$ $21.592$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q-2q^{3}-\zeta_{6}q^{5}+q^{9}+2\zeta_{6}q^{15}-3q^{17}+\cdots$$
2704.2.f.c $2$ $21.592$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+2iq^{5}-iq^{7}-2q^{9}+iq^{11}+\cdots$$
2704.2.f.d $2$ $21.592$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}-3iq^{5}-iq^{7}-2q^{9}+6iq^{11}+\cdots$$
2704.2.f.e $2$ $21.592$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}-iq^{5}+5iq^{7}-2q^{9}-2iq^{11}+\cdots$$
2704.2.f.f $2$ $21.592$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{5}+iq^{7}-3q^{9}+iq^{11}-6q^{17}+\cdots$$
2704.2.f.g $2$ $21.592$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{5}-4iq^{7}-3q^{9}-4iq^{11}-3q^{17}+\cdots$$
2704.2.f.h $2$ $21.592$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}-\zeta_{6}q^{7}-2q^{9}+3\zeta_{6}q^{11}+3q^{17}+\cdots$$
2704.2.f.i $2$ $21.592$ $$\Q(\sqrt{-1})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+2q^{3}+3iq^{5}+4iq^{7}+q^{9}+6iq^{15}+\cdots$$
2704.2.f.j $2$ $21.592$ $$\Q(\sqrt{-1})$$ None $$0$$ $$6$$ $$0$$ $$0$$ $$q+3q^{3}+iq^{5}-iq^{7}+6q^{9}+2iq^{11}+\cdots$$
2704.2.f.k $4$ $21.592$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{5}+\beta _{1}q^{7}+(1+\cdots)q^{9}+\cdots$$
2704.2.f.l $4$ $21.592$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-\beta _{3}q^{3}+(-\beta _{1}-2\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
2704.2.f.m $6$ $21.592$ 6.0.153664.1 None $$0$$ $$-6$$ $$0$$ $$0$$ $$q+(-2+2\beta _{2}+\beta _{4})q^{3}+(2\beta _{1}-2\beta _{3}+\cdots)q^{5}+\cdots$$
2704.2.f.n $6$ $21.592$ 6.0.153664.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-1+2\beta _{2}+\beta _{4})q^{3}+(-\beta _{1}+3\beta _{5})q^{5}+\cdots$$
2704.2.f.o $6$ $21.592$ 6.0.153664.1 None $$0$$ $$4$$ $$0$$ $$0$$ $$q+(\beta _{2}+\beta _{4})q^{3}+(-\beta _{3}+\beta _{5})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots$$
2704.2.f.p $6$ $21.592$ 6.0.153664.1 None $$0$$ $$8$$ $$0$$ $$0$$ $$q+(2-\beta _{2}-\beta _{4})q^{3}+(\beta _{3}-\beta _{5})q^{5}+\beta _{3}q^{7}+\cdots$$
2704.2.f.q $8$ $21.592$ 8.0.195105024.2 None $$0$$ $$4$$ $$0$$ $$0$$ $$q+(1-\beta _{1})q^{3}+(\beta _{3}+\beta _{6}-\beta _{7})q^{5}+\beta _{7}q^{7}+\cdots$$
2704.2.f.r $12$ $21.592$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$-6$$ $$0$$ $$0$$ $$q+(-1+\beta _{4}+\beta _{6})q^{3}+(\beta _{1}+\beta _{7}+\beta _{8}+\cdots)q^{5}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(2704, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2704, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(52, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(104, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(169, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(208, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(338, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(676, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1352, [\chi])$$$$^{\oplus 2}$$