# Properties

 Label 3381.2 Level 3381 Weight 2 Dimension 294756 Nonzero newspaces 32 Sturm bound 1655808 Trace bound 5

## Defining parameters

 Level: $$N$$ = $$3381 = 3 \cdot 7^{2} \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$1655808$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3381))$$.

Total New Old
Modular forms 419232 298832 120400
Cusp forms 408673 294756 113917
Eisenstein series 10559 4076 6483

## Trace form

 $$294756q - 6q^{2} - 309q^{3} - 604q^{4} + 12q^{5} - 281q^{6} - 704q^{7} + 42q^{8} - 285q^{9} + O(q^{10})$$ $$294756q - 6q^{2} - 309q^{3} - 604q^{4} + 12q^{5} - 281q^{6} - 704q^{7} + 42q^{8} - 285q^{9} - 538q^{10} + 48q^{11} - 273q^{12} - 570q^{13} + 48q^{14} - 528q^{15} - 496q^{16} + 34q^{17} - 261q^{18} - 560q^{19} + 148q^{20} - 346q^{21} - 964q^{22} + 68q^{23} - 532q^{24} - 472q^{25} + 128q^{26} - 252q^{27} - 576q^{28} + 106q^{29} - 195q^{30} - 488q^{31} + 182q^{32} - 240q^{33} - 422q^{34} + 84q^{35} - 527q^{36} - 538q^{37} + 38q^{38} - 325q^{39} - 770q^{40} - 112q^{41} - 498q^{42} - 1062q^{43} - 182q^{44} - 360q^{45} - 644q^{46} + 40q^{47} - 513q^{48} - 948q^{49} - 8q^{50} - 411q^{51} - 822q^{52} - 40q^{53} - 305q^{54} - 786q^{55} - 300q^{56} - 464q^{57} - 668q^{58} + 92q^{59} - 531q^{60} - 670q^{61} + 168q^{62} - 324q^{63} - 1060q^{64} + 192q^{65} - 282q^{66} - 470q^{67} + 276q^{68} - 351q^{69} - 1284q^{70} + 96q^{71} - 389q^{72} - 570q^{73} + 202q^{74} - 330q^{75} - 208q^{76} + 144q^{77} - 591q^{78} - 358q^{79} + 294q^{80} - 413q^{81} - 562q^{82} - 80q^{83} - 724q^{84} - 906q^{85} - 128q^{86} - 467q^{87} - 850q^{88} - 144q^{89} - 898q^{90} - 836q^{91} + 72q^{92} - 1044q^{93} - 776q^{94} - 258q^{95} - 582q^{96} - 600q^{97} - 876q^{98} - 1105q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3381))$$

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
3381.2.a $$\chi_{3381}(1, \cdot)$$ 3381.2.a.a 1 1
3381.2.a.b 1
3381.2.a.c 1
3381.2.a.d 1
3381.2.a.e 1
3381.2.a.f 1
3381.2.a.g 1
3381.2.a.h 1
3381.2.a.i 1
3381.2.a.j 1
3381.2.a.k 1
3381.2.a.l 1
3381.2.a.m 1
3381.2.a.n 2
3381.2.a.o 2
3381.2.a.p 2
3381.2.a.q 2
3381.2.a.r 2
3381.2.a.s 2
3381.2.a.t 2
3381.2.a.u 2
3381.2.a.v 3
3381.2.a.w 4
3381.2.a.x 4
3381.2.a.y 5
3381.2.a.z 5
3381.2.a.ba 6
3381.2.a.bb 6
3381.2.a.bc 6
3381.2.a.bd 6
3381.2.a.be 8
3381.2.a.bf 8
3381.2.a.bg 10
3381.2.a.bh 10
3381.2.a.bi 10
3381.2.a.bj 10
3381.2.a.bk 10
3381.2.a.bl 10
3381.2.d $$\chi_{3381}(1910, \cdot)$$ n/a 292 1
3381.2.e $$\chi_{3381}(344, \cdot)$$ n/a 318 1
3381.2.h $$\chi_{3381}(1126, \cdot)$$ n/a 160 1
3381.2.i $$\chi_{3381}(1243, \cdot)$$ n/a 292 2
3381.2.j $$\chi_{3381}(1195, \cdot)$$ n/a 320 2
3381.2.m $$\chi_{3381}(275, \cdot)$$ n/a 624 2
3381.2.n $$\chi_{3381}(668, \cdot)$$ n/a 588 2
3381.2.q $$\chi_{3381}(484, \cdot)$$ n/a 1224 6
3381.2.r $$\chi_{3381}(883, \cdot)$$ n/a 1640 10
3381.2.s $$\chi_{3381}(160, \cdot)$$ n/a 1344 6
3381.2.v $$\chi_{3381}(827, \cdot)$$ n/a 2664 6
3381.2.w $$\chi_{3381}(461, \cdot)$$ n/a 2472 6
3381.2.z $$\chi_{3381}(277, \cdot)$$ n/a 2472 12
3381.2.ba $$\chi_{3381}(97, \cdot)$$ n/a 1600 10
3381.2.bd $$\chi_{3381}(638, \cdot)$$ n/a 3180 10
3381.2.be $$\chi_{3381}(146, \cdot)$$ n/a 3120 10
3381.2.bh $$\chi_{3381}(361, \cdot)$$ n/a 3200 20
3381.2.bk $$\chi_{3381}(47, \cdot)$$ n/a 4920 12
3381.2.bl $$\chi_{3381}(137, \cdot)$$ n/a 5328 12
3381.2.bo $$\chi_{3381}(229, \cdot)$$ n/a 2688 12
3381.2.br $$\chi_{3381}(215, \cdot)$$ n/a 6240 20
3381.2.bs $$\chi_{3381}(263, \cdot)$$ n/a 6240 20
3381.2.bv $$\chi_{3381}(19, \cdot)$$ n/a 3200 20
3381.2.bw $$\chi_{3381}(64, \cdot)$$ n/a 13440 60
3381.2.bz $$\chi_{3381}(41, \cdot)$$ n/a 26640 60
3381.2.ca $$\chi_{3381}(113, \cdot)$$ n/a 26640 60
3381.2.cd $$\chi_{3381}(34, \cdot)$$ n/a 13440 60
3381.2.ce $$\chi_{3381}(4, \cdot)$$ n/a 26880 120
3381.2.cf $$\chi_{3381}(10, \cdot)$$ n/a 26880 120
3381.2.ci $$\chi_{3381}(11, \cdot)$$ n/a 53280 120
3381.2.cj $$\chi_{3381}(26, \cdot)$$ n/a 53280 120

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3381))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3381)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(161))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(483))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1127))$$$$^{\oplus 2}$$