# Properties

 Label 2028.4.b Level $2028$ Weight $4$ Character orbit 2028.b Rep. character $\chi_{2028}(337,\cdot)$ Character field $\Q$ Dimension $78$ Newform subspaces $12$ Sturm bound $1456$ Trace bound $17$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2028 = 2^{2} \cdot 3 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 2028.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$12$$ Sturm bound: $$1456$$ Trace bound: $$17$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(2028, [\chi])$$.

Total New Old
Modular forms 1134 78 1056
Cusp forms 1050 78 972
Eisenstein series 84 0 84

## Trace form

 $$78 q + 6 q^{3} + 702 q^{9} + O(q^{10})$$ $$78 q + 6 q^{3} + 702 q^{9} + 96 q^{17} - 224 q^{23} - 2330 q^{25} + 54 q^{27} + 40 q^{29} + 784 q^{43} - 5730 q^{49} - 660 q^{51} + 1104 q^{53} - 840 q^{55} + 576 q^{61} + 168 q^{69} - 426 q^{75} - 2584 q^{77} + 516 q^{79} + 6318 q^{81} + 72 q^{87} + 6376 q^{95} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(2028, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2028.4.b.a $2$ $119.656$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-6$$ $$0$$ $$0$$ $$q-3q^{3}+3iq^{5}-2iq^{7}+9q^{9}+18iq^{11}+\cdots$$
2028.4.b.b $2$ $119.656$ $$\Q(\sqrt{-3})$$ None $$0$$ $$6$$ $$0$$ $$0$$ $$q+3q^{3}-2\zeta_{6}q^{5}-11\zeta_{6}q^{7}+9q^{9}+\cdots$$
2028.4.b.c $2$ $119.656$ $$\Q(\sqrt{-1})$$ None $$0$$ $$6$$ $$0$$ $$0$$ $$q+3q^{3}+9iq^{5}+4iq^{7}+9q^{9}+18iq^{11}+\cdots$$
2028.4.b.d $2$ $119.656$ $$\Q(\sqrt{-1})$$ None $$0$$ $$6$$ $$0$$ $$0$$ $$q+3q^{3}+iq^{5}-2^{4}iq^{7}+9q^{9}-34iq^{11}+\cdots$$
2028.4.b.e $4$ $119.656$ $$\Q(i, \sqrt{22})$$ None $$0$$ $$-12$$ $$0$$ $$0$$ $$q-3q^{3}+\beta _{2}q^{5}+(2\beta _{1}+3\beta _{2})q^{7}+9q^{9}+\cdots$$
2028.4.b.f $4$ $119.656$ $$\Q(i, \sqrt{10})$$ None $$0$$ $$12$$ $$0$$ $$0$$ $$q+3q^{3}+(6\beta _{1}-\beta _{2})q^{5}+(-2\beta _{1}-3\beta _{2}+\cdots)q^{7}+\cdots$$
2028.4.b.g $4$ $119.656$ $$\Q(\zeta_{12})$$ None $$0$$ $$12$$ $$0$$ $$0$$ $$q+3q^{3}+(4\zeta_{12}+3\zeta_{12}^{2})q^{5}+(-\zeta_{12}+\cdots)q^{7}+\cdots$$
2028.4.b.h $6$ $119.656$ $$\mathbb{Q}[x]/(x^{6} + \cdots)$$ None $$0$$ $$-18$$ $$0$$ $$0$$ $$q-3q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-\beta _{2}-\beta _{5})q^{7}+\cdots$$
2028.4.b.i $8$ $119.656$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$-24$$ $$0$$ $$0$$ $$q-3q^{3}-\beta _{3}q^{5}-\beta _{2}q^{7}+9q^{9}-\beta _{4}q^{11}+\cdots$$
2028.4.b.j $8$ $119.656$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$24$$ $$0$$ $$0$$ $$q+3q^{3}+\beta _{6}q^{5}+(-\beta _{1}-\beta _{6})q^{7}+9q^{9}+\cdots$$
2028.4.b.k $18$ $119.656$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None $$0$$ $$-54$$ $$0$$ $$0$$ $$q-3q^{3}+\beta _{13}q^{5}-\beta _{15}q^{7}+9q^{9}+\cdots$$
2028.4.b.l $18$ $119.656$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None $$0$$ $$54$$ $$0$$ $$0$$ $$q+3q^{3}+\beta _{12}q^{5}+\beta _{14}q^{7}+9q^{9}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(2028, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(2028, [\chi]) \simeq$$ $$S_{4}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(52, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(156, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(169, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(338, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(507, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(676, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(1014, [\chi])$$$$^{\oplus 2}$$