# Properties

 Label 14.13.d Level $14$ Weight $13$ Character orbit 14.d Rep. character $\chi_{14}(3,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $16$ Newform subspaces $1$ Sturm bound $26$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$14 = 2 \cdot 7$$ Weight: $$k$$ $$=$$ $$13$$ Character orbit: $$[\chi]$$ $$=$$ 14.d (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$26$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{13}(14, [\chi])$$.

Total New Old
Modular forms 52 16 36
Cusp forms 44 16 28
Eisenstein series 8 0 8

## Trace form

 $$16 q - 16384 q^{4} + 18144 q^{5} - 469720 q^{7} + 2362248 q^{9} + O(q^{10})$$ $$16 q - 16384 q^{4} + 18144 q^{5} - 469720 q^{7} + 2362248 q^{9} - 2290176 q^{10} + 2072088 q^{11} - 11501568 q^{14} - 27163728 q^{15} - 33554432 q^{16} - 101561040 q^{17} - 4592640 q^{18} + 174931848 q^{19} - 323731368 q^{21} + 62776320 q^{22} + 25630560 q^{23} + 242221056 q^{24} + 521205808 q^{25} - 1434682368 q^{26} + 350863360 q^{28} + 532360944 q^{29} - 2151917568 q^{30} + 4583818344 q^{31} + 6054957720 q^{33} - 1612540440 q^{35} - 9675767808 q^{36} + 5764524040 q^{37} - 149506560 q^{38} + 10526083272 q^{39} + 4690280448 q^{40} - 12685086720 q^{42} - 66929432000 q^{43} + 4243636224 q^{44} + 57253352184 q^{45} + 7203213312 q^{46} + 18116171640 q^{47} - 9977452064 q^{49} - 99248080896 q^{50} - 23299256376 q^{51} + 8269578240 q^{52} + 39134161800 q^{53} + 105152205312 q^{54} + 3623878656 q^{56} - 328243960080 q^{57} + 29637396480 q^{58} + 201845459088 q^{59} + 27815657472 q^{60} + 336780254328 q^{61} - 389095094520 q^{63} + 137438953472 q^{64} + 158322703896 q^{65} + 268884080640 q^{66} + 107767119920 q^{67} + 207997009920 q^{68} - 6077815296 q^{70} - 1150259029344 q^{71} - 9405726720 q^{72} - 738414283320 q^{73} + 4902778368 q^{74} + 1537028640000 q^{75} - 321203352960 q^{77} - 786088888320 q^{78} + 227632064768 q^{79} - 76101451776 q^{80} - 391984178400 q^{81} - 302578053120 q^{82} - 32685686784 q^{84} + 710209696080 q^{85} - 38105192448 q^{86} + 1957017683880 q^{87} - 64282951680 q^{88} - 2485007442792 q^{89} + 1803248333904 q^{91} - 104982773760 q^{92} - 458668768680 q^{93} - 2021298693120 q^{94} - 186503862960 q^{95} - 496068722688 q^{96} - 356371660800 q^{98} + 3921180354576 q^{99} + O(q^{100})$$

## Decomposition of $$S_{13}^{\mathrm{new}}(14, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
14.13.d.a $$16$$ $$12.796$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$18144$$ $$-469720$$ $$q+(-\beta _{2}-\beta _{4})q^{2}+(5\beta _{2}+2\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots$$

## Decomposition of $$S_{13}^{\mathrm{old}}(14, [\chi])$$ into lower level spaces

$$S_{13}^{\mathrm{old}}(14, [\chi]) \cong$$ $$S_{13}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 2}$$