# Properties

 Label 15.5.c Level 15 Weight 5 Character orbit c Rep. character $$\chi_{15}(11,\cdot)$$ Character field $$\Q$$ Dimension 6 Newform subspaces 1 Sturm bound 10 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$15 = 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$5$$ Character orbit: $$[\chi]$$ $$=$$ 15.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$10$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(15, [\chi])$$.

Total New Old
Modular forms 10 6 4
Cusp forms 6 6 0
Eisenstein series 4 0 4

## Trace form

 $$6q + 8q^{3} - 50q^{4} - 2q^{6} + 76q^{7} + 118q^{9} + O(q^{10})$$ $$6q + 8q^{3} - 50q^{4} - 2q^{6} + 76q^{7} + 118q^{9} + 50q^{10} - 452q^{12} - 424q^{13} + 50q^{15} + 802q^{16} + 1160q^{18} - 244q^{19} - 876q^{21} + 340q^{22} - 786q^{24} - 750q^{25} - 352q^{27} - 3764q^{28} + 2200q^{30} + 3772q^{31} + 4420q^{33} + 3124q^{34} - 7606q^{36} + 1896q^{37} - 1336q^{39} - 4650q^{40} - 1980q^{42} - 7384q^{43} + 1900q^{45} + 8196q^{46} + 14668q^{48} - 1318q^{49} - 8492q^{51} + 8976q^{52} - 278q^{54} - 1300q^{55} - 11584q^{57} - 23740q^{58} + 5050q^{60} + 6452q^{61} + 14796q^{63} + 3174q^{64} - 12760q^{66} + 13816q^{67} + 5472q^{69} - 2100q^{70} - 2040q^{72} + 596q^{73} - 1000q^{75} + 21348q^{76} - 1400q^{78} - 16124q^{79} + 5086q^{81} - 31240q^{82} - 14736q^{84} - 3100q^{85} - 4900q^{87} + 15660q^{88} + 7550q^{90} - 11632q^{91} - 8184q^{93} + 34924q^{94} + 14354q^{96} + 9756q^{97} + 9680q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(15, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
15.5.c.a $$6$$ $$1.551$$ $$\mathbb{Q}[x]/(x^{6} + \cdots)$$ None $$0$$ $$8$$ $$0$$ $$76$$ $$q+\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(-8+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 - 23 T^{2} + 264 T^{4} - 4684 T^{6} + 67584 T^{8} - 1507328 T^{10} + 16777216 T^{12}$$
$3$ $$1 - 8 T - 27 T^{2} + 504 T^{3} - 2187 T^{4} - 52488 T^{5} + 531441 T^{6}$$
$5$ $$( 1 + 125 T^{2} )^{3}$$
$7$ $$( 1 - 38 T + 4653 T^{2} - 114976 T^{3} + 11171853 T^{4} - 219062438 T^{5} + 13841287201 T^{6} )^{2}$$
$11$ $$1 - 34466 T^{2} + 627812895 T^{4} - 9331838759740 T^{6} + 134577269649570495 T^{8} -$$$$15\!\cdots\!26$$$$T^{10} +$$$$98\!\cdots\!41$$$$T^{12}$$
$13$ $$( 1 + 212 T + 97943 T^{2} + 12289064 T^{3} + 2797350023 T^{4} + 172934912852 T^{5} + 23298085122481 T^{6} )^{2}$$
$17$ $$1 - 256778 T^{2} + 40830133839 T^{4} - 4057376310317644 T^{6} +$$$$28\!\cdots\!99$$$$T^{8} -$$$$12\!\cdots\!18$$$$T^{10} +$$$$33\!\cdots\!21$$$$T^{12}$$
$19$ $$( 1 + 122 T + 284939 T^{2} + 25213796 T^{3} + 37133535419 T^{4} + 2071994691002 T^{5} + 2213314919066161 T^{6} )^{2}$$
$23$ $$1 - 541878 T^{2} - 37441234461 T^{4} + 62508481606281076 T^{6} -$$$$29\!\cdots\!41$$$$T^{8} -$$$$33\!\cdots\!58$$$$T^{10} +$$$$48\!\cdots\!41$$$$T^{12}$$
$29$ $$1 - 1427666 T^{2} + 445361323935 T^{4} + 117229967968878500 T^{6} +$$$$22\!\cdots\!35$$$$T^{8} -$$$$35\!\cdots\!86$$$$T^{10} +$$$$12\!\cdots\!81$$$$T^{12}$$
$31$ $$( 1 - 1886 T + 3804195 T^{2} - 3654810940 T^{3} + 3513253970595 T^{4} - 1608552496613726 T^{5} + 787662783788549761 T^{6} )^{2}$$
$37$ $$( 1 - 948 T + 3630423 T^{2} - 3404430056 T^{3} + 6803997200103 T^{4} - 3329830522317108 T^{5} + 6582952005840035281 T^{6} )^{2}$$
$41$ $$1 - 9622286 T^{2} + 49511941482495 T^{4} -$$$$17\!\cdots\!40$$$$T^{6} +$$$$39\!\cdots\!95$$$$T^{8} -$$$$61\!\cdots\!26$$$$T^{10} +$$$$50\!\cdots\!61$$$$T^{12}$$
$43$ $$( 1 + 3692 T + 9012053 T^{2} + 15407946584 T^{3} + 30810415808453 T^{4} + 43152835424902892 T^{5} + 39959630797262576401 T^{6} )^{2}$$
$47$ $$1 - 19358678 T^{2} + 191449450821219 T^{4} -$$$$11\!\cdots\!24$$$$T^{6} +$$$$45\!\cdots\!59$$$$T^{8} -$$$$10\!\cdots\!38$$$$T^{10} +$$$$13\!\cdots\!81$$$$T^{12}$$
$53$ $$1 - 31471178 T^{2} + 496434526631919 T^{4} -$$$$48\!\cdots\!24$$$$T^{6} +$$$$30\!\cdots\!59$$$$T^{8} -$$$$12\!\cdots\!38$$$$T^{10} +$$$$24\!\cdots\!81$$$$T^{12}$$
$59$ $$1 - 20221586 T^{2} + 518070122195295 T^{4} -$$$$58\!\cdots\!40$$$$T^{6} +$$$$76\!\cdots\!95$$$$T^{8} -$$$$43\!\cdots\!26$$$$T^{10} +$$$$31\!\cdots\!61$$$$T^{12}$$
$61$ $$( 1 - 3226 T + 32346515 T^{2} - 81211143220 T^{3} + 447864703594115 T^{4} - 618447791729228506 T^{5} +$$$$26\!\cdots\!21$$$$T^{6} )^{2}$$
$67$ $$( 1 - 6908 T + 65136693 T^{2} - 250302748936 T^{3} + 1312577382182853 T^{4} - 2805115516561276028 T^{5} +$$$$81\!\cdots\!61$$$$T^{6} )^{2}$$
$71$ $$1 - 121682966 T^{2} + 6612859983587535 T^{4} -$$$$21\!\cdots\!00$$$$T^{6} +$$$$42\!\cdots\!35$$$$T^{8} -$$$$50\!\cdots\!86$$$$T^{10} +$$$$26\!\cdots\!81$$$$T^{12}$$
$73$ $$( 1 - 298 T + 50688863 T^{2} - 79767435436 T^{3} + 1439474547489983 T^{4} - 240325107384436138 T^{5} +$$$$22\!\cdots\!21$$$$T^{6} )^{2}$$
$79$ $$( 1 + 8062 T + 112728699 T^{2} + 533077126316 T^{3} + 4390791957074619 T^{4} + 12230931225466694782 T^{5} +$$$$59\!\cdots\!41$$$$T^{6} )^{2}$$
$83$ $$1 - 211578198 T^{2} + 21276155528463939 T^{4} -$$$$12\!\cdots\!04$$$$T^{6} +$$$$47\!\cdots\!99$$$$T^{8} -$$$$10\!\cdots\!38$$$$T^{10} +$$$$11\!\cdots\!21$$$$T^{12}$$
$89$ $$1 - 255353766 T^{2} + 32750513998015695 T^{4} -$$$$25\!\cdots\!40$$$$T^{6} +$$$$12\!\cdots\!95$$$$T^{8} -$$$$39\!\cdots\!26$$$$T^{10} +$$$$61\!\cdots\!41$$$$T^{12}$$
$97$ $$( 1 - 4878 T + 170499663 T^{2} - 362588117636 T^{3} + 15094212576132303 T^{4} - 38231001073370815758 T^{5} +$$$$69\!\cdots\!41$$$$T^{6} )^{2}$$