# Properties

 Label 5.7.c Level 5 Weight 7 Character orbit c Rep. character $$\chi_{5}(2,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 4 Newform subspaces 1 Sturm bound 3 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$5$$ Weight: $$k$$ $$=$$ $$7$$ Character orbit: $$[\chi]$$ $$=$$ 5.c (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$3$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{7}(5, [\chi])$$.

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

## Trace form

 $$4q - 10q^{2} + 30q^{3} - 70q^{5} - 552q^{6} + 550q^{7} + 1860q^{8} + O(q^{10})$$ $$4q - 10q^{2} + 30q^{3} - 70q^{5} - 552q^{6} + 550q^{7} + 1860q^{8} - 4370q^{10} - 1052q^{11} + 3480q^{12} + 1960q^{13} - 90q^{15} - 776q^{16} - 3280q^{17} - 870q^{18} + 20340q^{20} + 3828q^{21} - 27520q^{22} - 39010q^{23} + 30400q^{25} + 44068q^{26} + 31320q^{27} - 4840q^{28} - 50640q^{30} - 33172q^{31} - 48760q^{32} + 22260q^{33} - 24970q^{35} - 40836q^{36} + 146860q^{37} + 218040q^{38} - 110100q^{40} - 213932q^{41} - 31680q^{42} - 72050q^{43} + 78210q^{45} + 323288q^{46} + 830q^{47} - 74160q^{48} - 203350q^{50} - 172212q^{51} - 173300q^{52} - 29620q^{53} + 470660q^{55} + 467280q^{56} + 195840q^{57} - 554640q^{58} + 620280q^{60} - 111052q^{61} - 610520q^{62} - 350130q^{63} - 406540q^{65} - 457824q^{66} - 146930q^{67} + 775780q^{68} - 133320q^{70} + 1310188q^{71} + 899460q^{72} + 553540q^{73} - 435450q^{75} - 2073840q^{76} - 476300q^{77} + 268200q^{78} - 1011520q^{80} - 624816q^{81} + 2554880q^{82} + 536870q^{83} - 1344920q^{85} + 1019128q^{86} - 763440q^{87} - 187680q^{88} + 947310q^{90} + 1131548q^{91} - 2552680q^{92} + 444660q^{93} + 912600q^{95} - 568992q^{96} - 59420q^{97} - 1892810q^{98} + O(q^{100})$$

## Decomposition of $$S_{7}^{\mathrm{new}}(5, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
5.7.c.a $$4$$ $$1.150$$ $$\Q(i, \sqrt{201})$$ None $$-10$$ $$30$$ $$-70$$ $$550$$ $$q+(-2+2\beta _{1}+\beta _{3})q^{2}+(7+8\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + 10 T + 50 T^{2} - 240 T^{3} - 6592 T^{4} - 15360 T^{5} + 204800 T^{6} + 2621440 T^{7} + 16777216 T^{8}$$
$3$ $$1 - 30 T + 450 T^{2} - 22230 T^{3} + 1098018 T^{4} - 16205670 T^{5} + 239148450 T^{6} - 11622614670 T^{7} + 282429536481 T^{8}$$
$5$ $$1 + 70 T - 12750 T^{2} + 1093750 T^{3} + 244140625 T^{4}$$
$7$ $$1 - 550 T + 151250 T^{2} - 78815550 T^{3} + 40412328098 T^{4} - 9272570641950 T^{5} + 2093494689151250 T^{6} - 895627478850746950 T^{7} +$$$$19\!\cdots\!01$$$$T^{8}$$
$11$ $$( 1 + 526 T + 2481666 T^{2} + 931841086 T^{3} + 3138428376721 T^{4} )^{2}$$
$13$ $$1 - 1960 T + 1920800 T^{2} - 6864764760 T^{3} + 22780068732638 T^{4} - 33134908326450840 T^{5} + 44750961903261504800 T^{6} -$$$$22\!\cdots\!40$$$$T^{7} +$$$$54\!\cdots\!61$$$$T^{8}$$
$17$ $$1 + 3280 T + 5379200 T^{2} + 52715999280 T^{3} + 451561024170878 T^{4} + 1272436070024950320 T^{5} +$$$$31\!\cdots\!00$$$$T^{6} +$$$$46\!\cdots\!20$$$$T^{7} +$$$$33\!\cdots\!21$$$$T^{8}$$
$19$ $$1 - 55109524 T^{2} + 4864046077848966 T^{4} -$$$$12\!\cdots\!64$$$$T^{6} +$$$$48\!\cdots\!21$$$$T^{8}$$
$23$ $$1 + 39010 T + 760890050 T^{2} + 12796505733210 T^{3} + 182810834786595458 T^{4} +$$$$18\!\cdots\!90$$$$T^{5} +$$$$16\!\cdots\!50$$$$T^{6} +$$$$12\!\cdots\!90$$$$T^{7} +$$$$48\!\cdots\!41$$$$T^{8}$$
$29$ $$1 - 1657037284 T^{2} + 1284148562793102246 T^{4} -$$$$58\!\cdots\!44$$$$T^{6} +$$$$12\!\cdots\!81$$$$T^{8}$$
$31$ $$( 1 + 16586 T + 1245680586 T^{2} + 14720136053066 T^{3} + 787662783788549761 T^{4} )^{2}$$
$37$ $$1 - 146860 T + 10783929800 T^{2} - 657351006913860 T^{3} + 36420548331850749038 T^{4} -$$$$16\!\cdots\!40$$$$T^{5} +$$$$70\!\cdots\!00$$$$T^{6} -$$$$24\!\cdots\!40$$$$T^{7} +$$$$43\!\cdots\!61$$$$T^{8}$$
$41$ $$( 1 + 106966 T + 7285264146 T^{2} + 508099650242806 T^{3} + 22563490300366186081 T^{4} )^{2}$$
$43$ $$1 + 72050 T + 2595601250 T^{2} + 482755757677050 T^{3} + 89644137077771169698 T^{4} +$$$$30\!\cdots\!50$$$$T^{5} +$$$$10\!\cdots\!50$$$$T^{6} +$$$$18\!\cdots\!50$$$$T^{7} +$$$$15\!\cdots\!01$$$$T^{8}$$
$47$ $$1 - 830 T + 344450 T^{2} - 6853931089830 T^{3} +$$$$13\!\cdots\!18$$$$T^{4} -$$$$73\!\cdots\!70$$$$T^{5} +$$$$40\!\cdots\!50$$$$T^{6} -$$$$10\!\cdots\!70$$$$T^{7} +$$$$13\!\cdots\!81$$$$T^{8}$$
$53$ $$1 + 29620 T + 438672200 T^{2} + 493381118739420 T^{3} +$$$$52\!\cdots\!18$$$$T^{4} +$$$$10\!\cdots\!80$$$$T^{5} +$$$$21\!\cdots\!00$$$$T^{6} +$$$$32\!\cdots\!80$$$$T^{7} +$$$$24\!\cdots\!81$$$$T^{8}$$
$59$ $$1 - 166570372564 T^{2} +$$$$10\!\cdots\!86$$$$T^{4} -$$$$29\!\cdots\!84$$$$T^{6} +$$$$31\!\cdots\!61$$$$T^{8}$$
$61$ $$( 1 + 55526 T + 101522017266 T^{2} + 2860720306768886 T^{3} +$$$$26\!\cdots\!21$$$$T^{4} )^{2}$$
$67$ $$1 + 146930 T + 10794212450 T^{2} + 2898062262927930 T^{3} -$$$$42\!\cdots\!22$$$$T^{4} +$$$$26\!\cdots\!70$$$$T^{5} +$$$$88\!\cdots\!50$$$$T^{6} +$$$$10\!\cdots\!70$$$$T^{7} +$$$$66\!\cdots\!21$$$$T^{8}$$
$71$ $$( 1 - 655094 T + 342881964426 T^{2} - 83917727394943574 T^{3} +$$$$16\!\cdots\!41$$$$T^{4} )^{2}$$
$73$ $$1 - 553540 T + 153203265800 T^{2} - 75685034633171340 T^{3} +$$$$37\!\cdots\!58$$$$T^{4} -$$$$11\!\cdots\!60$$$$T^{5} +$$$$35\!\cdots\!00$$$$T^{6} -$$$$19\!\cdots\!60$$$$T^{7} +$$$$52\!\cdots\!41$$$$T^{8}$$
$79$ $$1 - 713041150084 T^{2} +$$$$23\!\cdots\!46$$$$T^{4} -$$$$42\!\cdots\!44$$$$T^{6} +$$$$34\!\cdots\!81$$$$T^{8}$$
$83$ $$1 - 536870 T + 144114698450 T^{2} + 4448869644102930 T^{3} -$$$$11\!\cdots\!22$$$$T^{4} +$$$$14\!\cdots\!70$$$$T^{5} +$$$$15\!\cdots\!50$$$$T^{6} -$$$$18\!\cdots\!30$$$$T^{7} +$$$$11\!\cdots\!21$$$$T^{8}$$
$89$ $$1 - 1229834859844 T^{2} +$$$$77\!\cdots\!26$$$$T^{4} -$$$$30\!\cdots\!24$$$$T^{6} +$$$$61\!\cdots\!41$$$$T^{8}$$
$97$ $$1 + 59420 T + 1765368200 T^{2} + 49275595300926420 T^{3} +$$$$13\!\cdots\!18$$$$T^{4} +$$$$41\!\cdots\!80$$$$T^{5} +$$$$12\!\cdots\!00$$$$T^{6} +$$$$34\!\cdots\!80$$$$T^{7} +$$$$48\!\cdots\!81$$$$T^{8}$$