Properties

Label 3267.2
Level 3267
Weight 2
Dimension 302413
Nonzero newspaces 24
Sturm bound 1568160
Trace bound 7

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Defining parameters

Level: \( N \) = \( 3267 = 3^{3} \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(1568160\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3267))\).

Total New Old
Modular forms 396840 306909 89931
Cusp forms 387241 302413 84828
Eisenstein series 9599 4496 5103

Trace form

\( 302413 q - 366 q^{2} - 546 q^{3} - 638 q^{4} - 363 q^{5} - 540 q^{6} - 637 q^{7} - 354 q^{8} - 540 q^{9} + O(q^{10}) \) \( 302413 q - 366 q^{2} - 546 q^{3} - 638 q^{4} - 363 q^{5} - 540 q^{6} - 637 q^{7} - 354 q^{8} - 540 q^{9} - 633 q^{10} - 400 q^{11} - 1008 q^{12} - 631 q^{13} - 345 q^{14} - 531 q^{15} - 626 q^{16} - 351 q^{17} - 531 q^{18} - 640 q^{19} - 323 q^{20} - 552 q^{21} - 700 q^{22} - 672 q^{23} - 558 q^{24} - 592 q^{25} - 310 q^{26} - 549 q^{27} - 1330 q^{28} - 306 q^{29} - 549 q^{30} - 591 q^{31} - 200 q^{32} - 600 q^{33} - 1101 q^{34} - 248 q^{35} - 522 q^{36} - 582 q^{37} - 198 q^{38} - 507 q^{39} - 489 q^{40} - 285 q^{41} - 522 q^{42} - 579 q^{43} - 370 q^{44} - 1029 q^{45} - 633 q^{46} - 375 q^{47} - 555 q^{48} - 624 q^{49} - 293 q^{50} - 558 q^{51} - 551 q^{52} - 298 q^{53} - 594 q^{54} - 1560 q^{55} - 513 q^{56} - 543 q^{57} - 449 q^{58} - 232 q^{59} - 540 q^{60} - 539 q^{61} - 72 q^{62} - 531 q^{63} - 466 q^{64} - 177 q^{65} - 600 q^{66} - 1040 q^{67} - 51 q^{68} - 531 q^{69} - 405 q^{70} - 173 q^{71} - 522 q^{72} - 551 q^{73} - 47 q^{74} - 501 q^{75} - 504 q^{76} - 320 q^{77} - 1002 q^{78} - 575 q^{79} - 958 q^{80} - 624 q^{81} - 1492 q^{82} - 601 q^{83} - 1014 q^{84} - 977 q^{85} - 969 q^{86} - 831 q^{87} - 1020 q^{88} - 1171 q^{89} - 1122 q^{90} - 869 q^{91} - 1519 q^{92} - 879 q^{93} - 1285 q^{94} - 1193 q^{95} - 1500 q^{96} - 966 q^{97} - 1405 q^{98} - 840 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3267))\)

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
3267.2.a \(\chi_{3267}(1, \cdot)\) 3267.2.a.a 1 1
3267.2.a.b 1
3267.2.a.c 1
3267.2.a.d 1
3267.2.a.e 1
3267.2.a.f 1
3267.2.a.g 1
3267.2.a.h 1
3267.2.a.i 1
3267.2.a.j 1
3267.2.a.k 1
3267.2.a.l 2
3267.2.a.m 2
3267.2.a.n 2
3267.2.a.o 2
3267.2.a.p 2
3267.2.a.q 2
3267.2.a.r 3
3267.2.a.s 3
3267.2.a.t 3
3267.2.a.u 3
3267.2.a.v 3
3267.2.a.w 3
3267.2.a.x 4
3267.2.a.y 4
3267.2.a.z 4
3267.2.a.ba 4
3267.2.a.bb 4
3267.2.a.bc 6
3267.2.a.bd 6
3267.2.a.be 8
3267.2.a.bf 8
3267.2.a.bg 8
3267.2.a.bh 8
3267.2.a.bi 8
3267.2.a.bj 8
3267.2.a.bk 8
3267.2.a.bl 8
3267.2.a.bm 8
3267.2.d \(\chi_{3267}(3266, \cdot)\) n/a 144 1
3267.2.e \(\chi_{3267}(1090, \cdot)\) n/a 200 2
3267.2.f \(\chi_{3267}(487, \cdot)\) n/a 576 4
3267.2.g \(\chi_{3267}(1088, \cdot)\) n/a 200 2
3267.2.j \(\chi_{3267}(364, \cdot)\) n/a 1908 6
3267.2.k \(\chi_{3267}(161, \cdot)\) n/a 576 4
3267.2.n \(\chi_{3267}(298, \cdot)\) n/a 1760 10
3267.2.o \(\chi_{3267}(856, \cdot)\) n/a 800 8
3267.2.p \(\chi_{3267}(362, \cdot)\) n/a 1896 6
3267.2.s \(\chi_{3267}(296, \cdot)\) n/a 1760 10
3267.2.x \(\chi_{3267}(233, \cdot)\) n/a 800 8
3267.2.y \(\chi_{3267}(100, \cdot)\) n/a 2600 20
3267.2.z \(\chi_{3267}(124, \cdot)\) n/a 7584 24
3267.2.ba \(\chi_{3267}(82, \cdot)\) n/a 7040 40
3267.2.bd \(\chi_{3267}(98, \cdot)\) n/a 2600 20
3267.2.bg \(\chi_{3267}(239, \cdot)\) n/a 7584 24
3267.2.bh \(\chi_{3267}(34, \cdot)\) n/a 23640 60
3267.2.bk \(\chi_{3267}(107, \cdot)\) n/a 7040 40
3267.2.bl \(\chi_{3267}(37, \cdot)\) n/a 10400 80
3267.2.bo \(\chi_{3267}(32, \cdot)\) n/a 23640 60
3267.2.bp \(\chi_{3267}(8, \cdot)\) n/a 10400 80
3267.2.bs \(\chi_{3267}(4, \cdot)\) n/a 94560 240
3267.2.bt \(\chi_{3267}(2, \cdot)\) n/a 94560 240

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3267))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3267)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(297))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1089))\)\(^{\oplus 2}\)