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Properties

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

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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

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

Display 100 coefficients 10 coefficients

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 available 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

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