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Properties

Label 3087.2
Level 3087
Weight 2
Dimension 260712
Nonzero newspaces 30
Sturm bound 1382976
Trace bound 9

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Defining parameters

Level: \( N \) = \( 3087 = 3^{2} \cdot 7^{3} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(1382976\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3087))\).

Total New Old
Modular forms 350112 264600 85512
Cusp forms 341377 260712 80665
Eisenstein series 8735 3888 4847

Trace form

\( 260712 q - 324 q^{2} - 432 q^{3} - 328 q^{4} - 327 q^{5} - 432 q^{6} - 378 q^{7} - 612 q^{8} - 432 q^{9} + O(q^{10}) \) \( 260712 q - 324 q^{2} - 432 q^{3} - 328 q^{4} - 327 q^{5} - 432 q^{6} - 378 q^{7} - 612 q^{8} - 432 q^{9} - 987 q^{10} - 333 q^{11} - 420 q^{12} - 331 q^{13} - 378 q^{14} - 792 q^{15} - 312 q^{16} - 303 q^{17} - 408 q^{18} - 961 q^{19} - 279 q^{20} - 504 q^{21} - 585 q^{22} - 309 q^{23} - 396 q^{24} - 324 q^{25} - 291 q^{26} - 414 q^{27} - 1134 q^{28} - 603 q^{29} - 390 q^{30} - 325 q^{31} - 276 q^{32} - 408 q^{33} - 303 q^{34} - 378 q^{35} - 744 q^{36} - 903 q^{37} - 177 q^{38} - 396 q^{39} - 15 q^{40} - 171 q^{41} - 504 q^{42} - 509 q^{43} + 3 q^{44} - 384 q^{45} - 669 q^{46} - 213 q^{47} - 444 q^{48} - 294 q^{49} - 678 q^{50} - 432 q^{51} + q^{52} - 273 q^{53} - 462 q^{54} - 783 q^{55} - 252 q^{56} - 852 q^{57} - 183 q^{58} - 327 q^{59} - 534 q^{60} - 239 q^{61} - 387 q^{62} - 504 q^{63} - 1738 q^{64} - 387 q^{65} - 474 q^{66} - 327 q^{67} - 435 q^{68} - 456 q^{69} - 378 q^{70} - 597 q^{71} - 486 q^{72} - 931 q^{73} - 303 q^{74} - 420 q^{75} - 277 q^{76} - 378 q^{77} - 768 q^{78} - 279 q^{79} - 153 q^{80} - 348 q^{81} - 717 q^{82} - 81 q^{83} - 504 q^{84} - 393 q^{85} + 105 q^{86} - 342 q^{87} + 225 q^{88} - 15 q^{89} - 270 q^{90} - 1050 q^{91} - 159 q^{92} - 318 q^{93} + 153 q^{94} + 135 q^{95} - 420 q^{96} - 49 q^{97} - 84 q^{98} - 1044 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3087))\)

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
3087.2.a \(\chi_{3087}(1, \cdot)\) 3087.2.a.a 3 1
3087.2.a.b 3
3087.2.a.c 3
3087.2.a.d 3
3087.2.a.e 3
3087.2.a.f 3
3087.2.a.g 6
3087.2.a.h 6
3087.2.a.i 6
3087.2.a.j 6
3087.2.a.k 6
3087.2.a.l 9
3087.2.a.m 9
3087.2.a.n 9
3087.2.a.o 9
3087.2.a.p 12
3087.2.a.q 12
3087.2.a.r 12
3087.2.c \(\chi_{3087}(3086, \cdot)\) 3087.2.c.a 12 1
3087.2.c.b 12
3087.2.c.c 24
3087.2.c.d 48
3087.2.e \(\chi_{3087}(361, \cdot)\) n/a 240 2
3087.2.f \(\chi_{3087}(1030, \cdot)\) n/a 576 2
3087.2.g \(\chi_{3087}(1390, \cdot)\) n/a 576 2
3087.2.h \(\chi_{3087}(1696, \cdot)\) n/a 576 2
3087.2.i \(\chi_{3087}(668, \cdot)\) n/a 576 2
3087.2.o \(\chi_{3087}(1028, \cdot)\) n/a 576 2
3087.2.p \(\chi_{3087}(2420, \cdot)\) n/a 192 2
3087.2.s \(\chi_{3087}(362, \cdot)\) n/a 576 2
3087.2.u \(\chi_{3087}(442, \cdot)\) n/a 666 6
3087.2.w \(\chi_{3087}(440, \cdot)\) n/a 552 6
3087.2.y \(\chi_{3087}(214, \cdot)\) n/a 3240 12
3087.2.z \(\chi_{3087}(67, \cdot)\) n/a 3240 12
3087.2.ba \(\chi_{3087}(148, \cdot)\) n/a 3240 12
3087.2.bb \(\chi_{3087}(226, \cdot)\) n/a 1344 12
3087.2.bd \(\chi_{3087}(374, \cdot)\) n/a 3240 12
3087.2.bg \(\chi_{3087}(80, \cdot)\) n/a 1128 12
3087.2.bh \(\chi_{3087}(146, \cdot)\) n/a 3240 12
3087.2.bn \(\chi_{3087}(68, \cdot)\) n/a 3240 12
3087.2.bo \(\chi_{3087}(64, \cdot)\) n/a 6846 42
3087.2.bq \(\chi_{3087}(62, \cdot)\) n/a 5544 42
3087.2.bs \(\chi_{3087}(25, \cdot)\) n/a 32760 84
3087.2.bt \(\chi_{3087}(37, \cdot)\) n/a 13608 84
3087.2.bu \(\chi_{3087}(4, \cdot)\) n/a 32760 84
3087.2.bv \(\chi_{3087}(22, \cdot)\) n/a 32760 84
3087.2.bw \(\chi_{3087}(20, \cdot)\) n/a 32760 84
3087.2.cc \(\chi_{3087}(47, \cdot)\) n/a 32760 84
3087.2.ce \(\chi_{3087}(17, \cdot)\) n/a 10920 84
3087.2.cf \(\chi_{3087}(5, \cdot)\) n/a 32760 84

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3087))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3087)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(343))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1029))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3087))\)\(^{\oplus 1}\)