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Properties

Label 3712.2
Level 3712
Weight 2
Dimension 240048
Nonzero newspaces 36
Sturm bound 1720320
Trace bound 22

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Defining parameters

Level: \( N \) = \( 3712 = 2^{7} \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(1720320\)
Trace bound: \(22\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3712))\).

Total New Old
Modular forms 434560 242640 191920
Cusp forms 425601 240048 185553
Eisenstein series 8959 2592 6367

Trace form

\( 240048 q - 416 q^{2} - 312 q^{3} - 416 q^{4} - 416 q^{5} - 416 q^{6} - 312 q^{7} - 416 q^{8} - 520 q^{9} + O(q^{10}) \) \( 240048 q - 416 q^{2} - 312 q^{3} - 416 q^{4} - 416 q^{5} - 416 q^{6} - 312 q^{7} - 416 q^{8} - 520 q^{9} - 416 q^{10} - 312 q^{11} - 416 q^{12} - 416 q^{13} - 416 q^{14} - 304 q^{15} - 416 q^{16} - 624 q^{17} - 416 q^{18} - 312 q^{19} - 416 q^{20} - 392 q^{21} - 416 q^{22} - 296 q^{23} - 416 q^{24} - 488 q^{25} - 416 q^{26} - 264 q^{27} - 416 q^{28} - 416 q^{29} - 864 q^{30} - 272 q^{31} - 416 q^{32} - 768 q^{33} - 416 q^{34} - 264 q^{35} - 416 q^{36} - 384 q^{37} - 416 q^{38} - 264 q^{39} - 416 q^{40} - 488 q^{41} - 416 q^{42} - 296 q^{43} - 416 q^{44} - 424 q^{45} - 416 q^{46} - 304 q^{47} - 416 q^{48} - 680 q^{49} - 512 q^{50} - 320 q^{51} - 608 q^{52} - 480 q^{53} - 672 q^{54} - 376 q^{55} - 640 q^{56} - 648 q^{57} - 576 q^{58} - 712 q^{59} - 800 q^{60} - 544 q^{61} - 608 q^{62} - 432 q^{63} - 800 q^{64} - 544 q^{65} - 800 q^{66} - 392 q^{67} - 608 q^{68} - 520 q^{69} - 800 q^{70} - 376 q^{71} - 704 q^{72} - 648 q^{73} - 640 q^{74} - 336 q^{75} - 672 q^{76} - 424 q^{77} - 608 q^{78} - 304 q^{79} - 512 q^{80} - 632 q^{81} - 416 q^{82} - 232 q^{83} - 416 q^{84} - 432 q^{85} - 416 q^{86} - 268 q^{87} - 864 q^{88} - 392 q^{89} - 416 q^{90} - 216 q^{91} - 416 q^{92} - 320 q^{93} - 416 q^{94} - 192 q^{95} - 416 q^{96} - 704 q^{97} - 416 q^{98} - 208 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3712))\)

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
3712.2.a \(\chi_{3712}(1, \cdot)\) 3712.2.a.a 1 1
3712.2.a.b 1
3712.2.a.c 1
3712.2.a.d 1
3712.2.a.e 1
3712.2.a.f 1
3712.2.a.g 1
3712.2.a.h 1
3712.2.a.i 1
3712.2.a.j 1
3712.2.a.k 1
3712.2.a.l 1
3712.2.a.m 1
3712.2.a.n 1
3712.2.a.o 1
3712.2.a.p 1
3712.2.a.q 2
3712.2.a.r 2
3712.2.a.s 2
3712.2.a.t 2
3712.2.a.u 5
3712.2.a.v 5
3712.2.a.w 5
3712.2.a.x 5
3712.2.a.y 5
3712.2.a.z 5
3712.2.a.ba 5
3712.2.a.bb 5
3712.2.a.bc 5
3712.2.a.bd 5
3712.2.a.be 5
3712.2.a.bf 5
3712.2.a.bg 7
3712.2.a.bh 7
3712.2.a.bi 7
3712.2.a.bj 7
3712.2.c \(\chi_{3712}(1857, \cdot)\) 3712.2.c.a 4 1
3712.2.c.b 8
3712.2.c.c 8
3712.2.c.d 20
3712.2.c.e 20
3712.2.c.f 24
3712.2.c.g 28
3712.2.e \(\chi_{3712}(3073, \cdot)\) n/a 120 1
3712.2.g \(\chi_{3712}(1217, \cdot)\) n/a 120 1
3712.2.j \(\chi_{3712}(1119, \cdot)\) n/a 232 2
3712.2.k \(\chi_{3712}(2047, \cdot)\) n/a 240 2
3712.2.m \(\chi_{3712}(289, \cdot)\) n/a 232 2
3712.2.n \(\chi_{3712}(929, \cdot)\) n/a 224 2
3712.2.q \(\chi_{3712}(191, \cdot)\) n/a 240 2
3712.2.t \(\chi_{3712}(1375, \cdot)\) n/a 232 2
3712.2.u \(\chi_{3712}(257, \cdot)\) n/a 720 6
3712.2.v \(\chi_{3712}(465, \cdot)\) n/a 448 4
3712.2.x \(\chi_{3712}(911, \cdot)\) n/a 472 4
3712.2.ba \(\chi_{3712}(655, \cdot)\) n/a 472 4
3712.2.bc \(\chi_{3712}(753, \cdot)\) n/a 472 4
3712.2.be \(\chi_{3712}(705, \cdot)\) n/a 720 6
3712.2.bg \(\chi_{3712}(129, \cdot)\) n/a 720 6
3712.2.bi \(\chi_{3712}(65, \cdot)\) n/a 720 6
3712.2.bl \(\chi_{3712}(679, \cdot)\) None 0 8
3712.2.bn \(\chi_{3712}(233, \cdot)\) None 0 8
3712.2.bp \(\chi_{3712}(57, \cdot)\) None 0 8
3712.2.bq \(\chi_{3712}(215, \cdot)\) None 0 8
3712.2.bs \(\chi_{3712}(31, \cdot)\) n/a 1392 12
3712.2.bv \(\chi_{3712}(831, \cdot)\) n/a 1440 12
3712.2.by \(\chi_{3712}(161, \cdot)\) n/a 1392 12
3712.2.bz \(\chi_{3712}(33, \cdot)\) n/a 1392 12
3712.2.cb \(\chi_{3712}(127, \cdot)\) n/a 1440 12
3712.2.cc \(\chi_{3712}(287, \cdot)\) n/a 1392 12
3712.2.ce \(\chi_{3712}(75, \cdot)\) n/a 7648 16
3712.2.cg \(\chi_{3712}(173, \cdot)\) n/a 7648 16
3712.2.ch \(\chi_{3712}(117, \cdot)\) n/a 7168 16
3712.2.ck \(\chi_{3712}(307, \cdot)\) n/a 7648 16
3712.2.cn \(\chi_{3712}(209, \cdot)\) n/a 2832 24
3712.2.cp \(\chi_{3712}(47, \cdot)\) n/a 2832 24
3712.2.cq \(\chi_{3712}(15, \cdot)\) n/a 2832 24
3712.2.cs \(\chi_{3712}(49, \cdot)\) n/a 2832 24
3712.2.cu \(\chi_{3712}(55, \cdot)\) None 0 48
3712.2.cw \(\chi_{3712}(9, \cdot)\) None 0 48
3712.2.cy \(\chi_{3712}(25, \cdot)\) None 0 48
3712.2.db \(\chi_{3712}(39, \cdot)\) None 0 48
3712.2.dd \(\chi_{3712}(3, \cdot)\) n/a 45888 96
3712.2.dg \(\chi_{3712}(45, \cdot)\) n/a 45888 96
3712.2.dh \(\chi_{3712}(5, \cdot)\) n/a 45888 96
3712.2.dj \(\chi_{3712}(11, \cdot)\) n/a 45888 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3712))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3712)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(232))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(464))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(928))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1856))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3712))\)\(^{\oplus 1}\)