# Properties

 Label 3971.2 Level 3971 Weight 2 Dimension 631220 Nonzero newspaces 24 Sturm bound 2599200 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$3971 = 11 \cdot 19^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Sturm bound: $$2599200$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3971))$$.

Total New Old
Modular forms 654840 639652 15188
Cusp forms 644761 631220 13541
Eisenstein series 10079 8432 1647

## Trace form

 $$631220 q - 1223 q^{2} - 1221 q^{3} - 1215 q^{4} - 1217 q^{5} - 1210 q^{6} - 1218 q^{7} - 1209 q^{8} - 1213 q^{9} + O(q^{10})$$ $$631220 q - 1223 q^{2} - 1221 q^{3} - 1215 q^{4} - 1217 q^{5} - 1210 q^{6} - 1218 q^{7} - 1209 q^{8} - 1213 q^{9} - 1208 q^{10} - 1375 q^{11} - 2776 q^{12} - 1254 q^{13} - 1268 q^{14} - 1273 q^{15} - 1341 q^{16} - 1244 q^{17} - 1325 q^{18} - 1338 q^{19} - 2476 q^{20} - 1274 q^{21} - 1430 q^{22} - 2767 q^{23} - 1308 q^{24} - 1269 q^{25} - 1262 q^{26} - 1263 q^{27} - 1328 q^{28} - 1266 q^{29} - 1402 q^{30} - 1257 q^{31} - 1333 q^{32} - 1482 q^{33} - 2876 q^{34} - 1322 q^{35} - 1569 q^{36} - 1291 q^{37} - 1422 q^{38} - 2540 q^{39} - 1458 q^{40} - 1262 q^{41} - 1492 q^{42} - 1342 q^{43} - 1512 q^{44} - 3002 q^{45} - 1474 q^{46} - 1348 q^{47} - 1600 q^{48} - 1326 q^{49} - 1519 q^{50} - 1366 q^{51} - 1382 q^{52} - 1320 q^{53} - 1438 q^{54} - 1442 q^{55} - 3102 q^{56} - 1386 q^{57} - 2430 q^{58} - 1339 q^{59} - 1670 q^{60} - 1414 q^{61} - 1538 q^{62} - 1452 q^{63} - 1657 q^{64} - 1532 q^{65} - 1651 q^{66} - 3065 q^{67} - 1606 q^{68} - 1523 q^{69} - 1652 q^{70} - 1407 q^{71} - 1821 q^{72} - 1482 q^{73} - 1476 q^{74} - 1468 q^{75} - 1476 q^{76} - 2865 q^{77} - 3154 q^{78} - 1562 q^{79} - 1690 q^{80} - 1570 q^{81} - 1766 q^{82} - 1398 q^{83} - 1860 q^{84} - 1550 q^{85} - 1476 q^{86} - 1680 q^{87} - 1686 q^{88} - 2973 q^{89} - 1814 q^{90} - 1456 q^{91} - 1526 q^{92} - 1511 q^{93} - 1564 q^{94} - 1422 q^{95} - 2996 q^{96} - 1385 q^{97} - 1731 q^{98} - 1636 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3971))$$

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
3971.2.a $$\chi_{3971}(1, \cdot)$$ 3971.2.a.a 1 1
3971.2.a.b 1
3971.2.a.c 2
3971.2.a.d 2
3971.2.a.e 3
3971.2.a.f 3
3971.2.a.g 4
3971.2.a.h 5
3971.2.a.i 7
3971.2.a.j 9
3971.2.a.k 9
3971.2.a.l 9
3971.2.a.m 9
3971.2.a.n 10
3971.2.a.o 10
3971.2.a.p 10
3971.2.a.q 18
3971.2.a.r 18
3971.2.a.s 21
3971.2.a.t 21
3971.2.a.u 24
3971.2.a.v 24
3971.2.a.w 24
3971.2.a.x 40
3971.2.d $$\chi_{3971}(3970, \cdot)$$ n/a 324 1
3971.2.e $$\chi_{3971}(2234, \cdot)$$ n/a 564 2
3971.2.f $$\chi_{3971}(1445, \cdot)$$ n/a 1296 4
3971.2.g $$\chi_{3971}(791, \cdot)$$ n/a 648 2
3971.2.j $$\chi_{3971}(595, \cdot)$$ n/a 1704 6
3971.2.k $$\chi_{3971}(360, \cdot)$$ n/a 1296 4
3971.2.n $$\chi_{3971}(653, \cdot)$$ n/a 2592 8
3971.2.p $$\chi_{3971}(307, \cdot)$$ n/a 1944 6
3971.2.r $$\chi_{3971}(210, \cdot)$$ n/a 5724 18
3971.2.u $$\chi_{3971}(293, \cdot)$$ n/a 2592 8
3971.2.v $$\chi_{3971}(208, \cdot)$$ n/a 6804 18
3971.2.y $$\chi_{3971}(234, \cdot)$$ n/a 7776 24
3971.2.z $$\chi_{3971}(45, \cdot)$$ n/a 11448 36
3971.2.bb $$\chi_{3971}(116, \cdot)$$ n/a 7776 24
3971.2.bd $$\chi_{3971}(20, \cdot)$$ n/a 27216 72
3971.2.bg $$\chi_{3971}(65, \cdot)$$ n/a 13608 36
3971.2.bh $$\chi_{3971}(23, \cdot)$$ n/a 34128 108
3971.2.bk $$\chi_{3971}(18, \cdot)$$ n/a 27216 72
3971.2.bl $$\chi_{3971}(26, \cdot)$$ n/a 54432 144
3971.2.bn $$\chi_{3971}(10, \cdot)$$ n/a 40824 108
3971.2.bp $$\chi_{3971}(8, \cdot)$$ n/a 54432 144
3971.2.bs $$\chi_{3971}(4, \cdot)$$ n/a 163296 432
3971.2.bu $$\chi_{3971}(2, \cdot)$$ n/a 163296 432

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3971))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3971)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(209))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(361))$$$$^{\oplus 2}$$