# Properties

 Label 1014.4.b Level $1014$ Weight $4$ Character orbit 1014.b Rep. character $\chi_{1014}(337,\cdot)$ Character field $\Q$ Dimension $78$ Newform subspaces $17$ Sturm bound $728$ Trace bound $10$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1014 = 2 \cdot 3 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1014.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$17$$ Sturm bound: $$728$$ Trace bound: $$10$$ Distinguishing $$T_p$$: $$5$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(1014, [\chi])$$.

Total New Old
Modular forms 574 78 496
Cusp forms 518 78 440
Eisenstein series 56 0 56

## Trace form

 $$78 q - 6 q^{3} - 312 q^{4} + 702 q^{9} + O(q^{10})$$ $$78 q - 6 q^{3} - 312 q^{4} + 702 q^{9} - 104 q^{10} + 24 q^{12} - 96 q^{14} + 1248 q^{16} + 192 q^{17} + 200 q^{22} - 8 q^{23} - 1658 q^{25} - 54 q^{27} - 56 q^{29} - 120 q^{30} + 1560 q^{35} - 2808 q^{36} - 704 q^{38} + 416 q^{40} + 168 q^{42} - 1064 q^{43} - 96 q^{48} - 3330 q^{49} + 348 q^{51} - 528 q^{53} - 336 q^{55} + 384 q^{56} - 2352 q^{61} - 2464 q^{62} - 4992 q^{64} + 1152 q^{66} - 768 q^{68} - 1992 q^{69} + 704 q^{74} + 1674 q^{75} + 1256 q^{77} + 3300 q^{79} + 6318 q^{81} + 224 q^{82} - 2736 q^{87} - 800 q^{88} - 936 q^{90} + 32 q^{92} + 1088 q^{94} - 224 q^{95} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(1014, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1014.4.b.a $2$ $59.828$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-6$$ $$0$$ $$0$$ $$q+iq^{2}-3q^{3}-4q^{4}+8iq^{5}-3iq^{6}+\cdots$$
1014.4.b.b $2$ $59.828$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-6$$ $$0$$ $$0$$ $$q+2iq^{2}-3q^{3}-4q^{4}+7iq^{5}-6iq^{6}+\cdots$$
1014.4.b.c $2$ $59.828$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-6$$ $$0$$ $$0$$ $$q+iq^{2}-3q^{3}-4q^{4}+3iq^{5}-3iq^{6}+\cdots$$
1014.4.b.d $2$ $59.828$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-6$$ $$0$$ $$0$$ $$q-iq^{2}-3q^{3}-4q^{4}+3iq^{5}+3iq^{6}+\cdots$$
1014.4.b.e $2$ $59.828$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-6$$ $$0$$ $$0$$ $$q-iq^{2}-3q^{3}-4q^{4}+10iq^{5}+3iq^{6}+\cdots$$
1014.4.b.f $2$ $59.828$ $$\Q(\sqrt{-1})$$ None $$0$$ $$6$$ $$0$$ $$0$$ $$q+iq^{2}+3q^{3}-4q^{4}+8iq^{5}+3iq^{6}+\cdots$$
1014.4.b.g $2$ $59.828$ $$\Q(\sqrt{-1})$$ None $$0$$ $$6$$ $$0$$ $$0$$ $$q+iq^{2}+3q^{3}-4q^{4}+2iq^{5}+3iq^{6}+\cdots$$
1014.4.b.h $2$ $59.828$ $$\Q(\sqrt{-1})$$ None $$0$$ $$6$$ $$0$$ $$0$$ $$q-iq^{2}+3q^{3}-4q^{4}+5iq^{5}-3iq^{6}+\cdots$$
1014.4.b.i $4$ $59.828$ $$\Q(i, \sqrt{61})$$ None $$0$$ $$-12$$ $$0$$ $$0$$ $$q-2\beta _{1}q^{2}-3q^{3}-4q^{4}+(\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots$$
1014.4.b.j $4$ $59.828$ $$\Q(i, \sqrt{673})$$ None $$0$$ $$12$$ $$0$$ $$0$$ $$q-2\beta _{2}q^{2}+3q^{3}-4q^{4}+(\beta _{1}-6\beta _{2}+\cdots)q^{5}+\cdots$$
1014.4.b.k $4$ $59.828$ $$\Q(\zeta_{12})$$ None $$0$$ $$12$$ $$0$$ $$0$$ $$q-2\zeta_{12}q^{2}+3q^{3}-4q^{4}+(6\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots$$
1014.4.b.l $6$ $59.828$ 6.0.153664.1 None $$0$$ $$-18$$ $$0$$ $$0$$ $$q+2\beta _{5}q^{2}-3q^{3}-4q^{4}+(-2\beta _{1}-3\beta _{3}+\cdots)q^{5}+\cdots$$
1014.4.b.m $6$ $59.828$ $$\mathbb{Q}[x]/(x^{6} + \cdots)$$ None $$0$$ $$18$$ $$0$$ $$0$$ $$q+2\beta _{2}q^{2}+3q^{3}-4q^{4}+(\beta _{1}+4\beta _{2}+\cdots)q^{5}+\cdots$$
1014.4.b.n $6$ $59.828$ 6.0.153664.1 None $$0$$ $$18$$ $$0$$ $$0$$ $$q+2\beta _{5}q^{2}+3q^{3}-4q^{4}+(3\beta _{1}+5\beta _{3}+\cdots)q^{5}+\cdots$$
1014.4.b.o $8$ $59.828$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$-24$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}-3q^{3}-4q^{4}+(3\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$$
1014.4.b.p $12$ $59.828$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$-36$$ $$0$$ $$0$$ $$q-2\beta _{7}q^{2}-3q^{3}-4q^{4}+(-\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots$$
1014.4.b.q $12$ $59.828$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$36$$ $$0$$ $$0$$ $$q-2\beta _{3}q^{2}+3q^{3}-4q^{4}+\beta _{8}q^{5}-6\beta _{3}q^{6}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(1014, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(1014, [\chi]) \simeq$$ $$S_{4}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(169, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(338, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(507, [\chi])$$$$^{\oplus 2}$$