# Properties

 Label 135.4.e Level $135$ Weight $4$ Character orbit 135.e Rep. character $\chi_{135}(46,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $24$ Newform subspaces $3$ Sturm bound $72$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$135 = 3^{3} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 135.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$3$$ Sturm bound: $$72$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(135, [\chi])$$.

Total New Old
Modular forms 120 24 96
Cusp forms 96 24 72
Eisenstein series 24 0 24

## Trace form

 $$24 q - 4 q^{2} - 48 q^{4} - 10 q^{5} + 12 q^{7} + 108 q^{8} + O(q^{10})$$ $$24 q - 4 q^{2} - 48 q^{4} - 10 q^{5} + 12 q^{7} + 108 q^{8} - 46 q^{11} - 24 q^{13} + 6 q^{14} - 192 q^{16} + 500 q^{17} + 300 q^{19} - 120 q^{20} - 36 q^{22} - 192 q^{23} - 300 q^{25} - 1432 q^{26} - 384 q^{28} + 286 q^{29} + 120 q^{31} + 484 q^{32} + 378 q^{34} + 560 q^{35} + 336 q^{37} - 88 q^{38} + 90 q^{40} + 472 q^{41} + 174 q^{43} - 1652 q^{44} + 540 q^{46} - 400 q^{47} - 1026 q^{49} - 100 q^{50} - 1302 q^{52} + 2024 q^{53} + 1530 q^{56} - 594 q^{58} - 298 q^{59} + 858 q^{61} + 1644 q^{62} + 2760 q^{64} - 840 q^{65} + 1362 q^{67} - 2732 q^{68} + 180 q^{70} - 272 q^{71} + 1812 q^{73} + 1480 q^{74} - 2598 q^{76} - 1056 q^{77} - 888 q^{79} + 4560 q^{80} - 3492 q^{82} - 2508 q^{83} - 360 q^{85} + 2762 q^{86} - 432 q^{88} - 7404 q^{89} + 3984 q^{91} - 4140 q^{92} + 1962 q^{94} - 2040 q^{95} - 474 q^{97} - 2696 q^{98} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(135, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
135.4.e.a $4$ $7.965$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$-1$$ $$0$$ $$10$$ $$-9$$ $$q+(-\beta _{1}+\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots$$
135.4.e.b $6$ $7.965$ 6.0.15759792.1 None $$-1$$ $$0$$ $$15$$ $$43$$ $$q+(-\beta _{1}-\beta _{4})q^{2}+(-\beta _{2}+3\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$$
135.4.e.c $14$ $7.965$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None $$-2$$ $$0$$ $$-35$$ $$-22$$ $$q+(\beta _{1}-\beta _{2})q^{2}+(-5-\beta _{3}-5\beta _{5}-\beta _{10}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(135, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(135, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(9, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(27, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 2}$$