Properties

Label 3675.2
Level 3675
Weight 2
Dimension 310043
Nonzero newspaces 48
Sturm bound 1881600
Trace bound 4

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Defining parameters

Level: \( N \) = \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(1881600\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3675))\).

Total New Old
Modular forms 477120 314019 163101
Cusp forms 463681 310043 153638
Eisenstein series 13439 3976 9463

Trace form

\( 310043 q - q^{2} - 206 q^{3} - 431 q^{4} - 6 q^{5} - 356 q^{6} - 476 q^{7} - 57 q^{8} - 222 q^{9} + O(q^{10}) \) \( 310043 q - q^{2} - 206 q^{3} - 431 q^{4} - 6 q^{5} - 356 q^{6} - 476 q^{7} - 57 q^{8} - 222 q^{9} - 514 q^{10} - 40 q^{11} - 240 q^{12} - 460 q^{13} - 24 q^{14} - 446 q^{15} - 735 q^{16} - 26 q^{17} - 202 q^{18} - 438 q^{19} + 36 q^{20} - 385 q^{21} - 758 q^{22} - 32 q^{23} + 6 q^{24} - 418 q^{25} + 102 q^{26} - 74 q^{27} - 348 q^{28} + 134 q^{29} - 82 q^{30} - 554 q^{31} + 461 q^{32} - 7 q^{33} - 62 q^{34} + 72 q^{35} - 182 q^{36} - 166 q^{37} + 368 q^{38} + 72 q^{39} - 190 q^{40} + 206 q^{41} - 21 q^{42} - 522 q^{43} + 516 q^{44} - 104 q^{45} - 330 q^{46} + 88 q^{47} + 285 q^{48} - 354 q^{49} + 106 q^{50} - 543 q^{51} + 204 q^{52} + 44 q^{53} - 86 q^{54} - 380 q^{55} + 342 q^{56} - 159 q^{57} + 392 q^{58} + 328 q^{59} + 14 q^{60} - 146 q^{61} + 688 q^{62} - 204 q^{63} + 201 q^{64} + 230 q^{65} + 125 q^{66} + 122 q^{67} + 670 q^{68} + 79 q^{69} - 216 q^{70} + 208 q^{71} - 24 q^{72} + 164 q^{73} + 718 q^{74} - 162 q^{75} - 494 q^{76} + 216 q^{77} + 107 q^{78} + 110 q^{79} + 278 q^{80} - 282 q^{81} + 434 q^{82} + 356 q^{83} - 4 q^{84} - 634 q^{85} + 422 q^{86} - 143 q^{87} + 508 q^{88} + 120 q^{89} - 456 q^{90} - 698 q^{91} - 10 q^{92} - 233 q^{93} - 164 q^{94} + 56 q^{95} - 777 q^{96} - 242 q^{97} + 438 q^{98} - 880 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3675))\)

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
3675.2.a \(\chi_{3675}(1, \cdot)\) 3675.2.a.a 1 1
3675.2.a.b 1
3675.2.a.c 1
3675.2.a.d 1
3675.2.a.e 1
3675.2.a.f 1
3675.2.a.g 1
3675.2.a.h 1
3675.2.a.i 1
3675.2.a.j 1
3675.2.a.k 1
3675.2.a.l 1
3675.2.a.m 1
3675.2.a.n 1
3675.2.a.o 1
3675.2.a.p 1
3675.2.a.q 1
3675.2.a.r 2
3675.2.a.s 2
3675.2.a.t 2
3675.2.a.u 2
3675.2.a.v 2
3675.2.a.w 2
3675.2.a.x 2
3675.2.a.y 2
3675.2.a.z 2
3675.2.a.ba 2
3675.2.a.bb 2
3675.2.a.bc 2
3675.2.a.bd 2
3675.2.a.be 2
3675.2.a.bf 2
3675.2.a.bg 2
3675.2.a.bh 2
3675.2.a.bi 3
3675.2.a.bj 3
3675.2.a.bk 4
3675.2.a.bl 4
3675.2.a.bm 4
3675.2.a.bn 4
3675.2.a.bo 4
3675.2.a.bp 4
3675.2.a.bq 4
3675.2.a.br 4
3675.2.a.bs 4
3675.2.a.bt 4
3675.2.a.bu 4
3675.2.a.bv 4
3675.2.a.bw 4
3675.2.a.bx 4
3675.2.a.by 4
3675.2.a.bz 4
3675.2.a.ca 4
3675.2.a.cb 4
3675.2.b \(\chi_{3675}(2351, \cdot)\) n/a 242 1
3675.2.d \(\chi_{3675}(1324, \cdot)\) n/a 124 1
3675.2.g \(\chi_{3675}(3674, \cdot)\) n/a 232 1
3675.2.i \(\chi_{3675}(226, \cdot)\) n/a 254 2
3675.2.j \(\chi_{3675}(932, \cdot)\) n/a 472 2
3675.2.m \(\chi_{3675}(832, \cdot)\) n/a 240 2
3675.2.n \(\chi_{3675}(736, \cdot)\) n/a 824 4
3675.2.q \(\chi_{3675}(374, \cdot)\) n/a 464 2
3675.2.r \(\chi_{3675}(949, \cdot)\) n/a 240 2
3675.2.t \(\chi_{3675}(2126, \cdot)\) n/a 482 2
3675.2.v \(\chi_{3675}(526, \cdot)\) n/a 1068 6
3675.2.x \(\chi_{3675}(734, \cdot)\) n/a 1568 4
3675.2.ba \(\chi_{3675}(589, \cdot)\) n/a 816 4
3675.2.bc \(\chi_{3675}(146, \cdot)\) n/a 1568 4
3675.2.bd \(\chi_{3675}(607, \cdot)\) n/a 480 4
3675.2.bg \(\chi_{3675}(557, \cdot)\) n/a 928 4
3675.2.bi \(\chi_{3675}(524, \cdot)\) n/a 1992 6
3675.2.bl \(\chi_{3675}(274, \cdot)\) n/a 1008 6
3675.2.bn \(\chi_{3675}(251, \cdot)\) n/a 2088 6
3675.2.bo \(\chi_{3675}(361, \cdot)\) n/a 1600 8
3675.2.bp \(\chi_{3675}(97, \cdot)\) n/a 1600 8
3675.2.bs \(\chi_{3675}(197, \cdot)\) n/a 3200 8
3675.2.bt \(\chi_{3675}(151, \cdot)\) n/a 2124 12
3675.2.bv \(\chi_{3675}(118, \cdot)\) n/a 2016 12
3675.2.bw \(\chi_{3675}(218, \cdot)\) n/a 3984 12
3675.2.bz \(\chi_{3675}(521, \cdot)\) n/a 3136 8
3675.2.cb \(\chi_{3675}(79, \cdot)\) n/a 1600 8
3675.2.cc \(\chi_{3675}(509, \cdot)\) n/a 3136 8
3675.2.cf \(\chi_{3675}(106, \cdot)\) n/a 6720 24
3675.2.ch \(\chi_{3675}(26, \cdot)\) n/a 4188 12
3675.2.cj \(\chi_{3675}(424, \cdot)\) n/a 2016 12
3675.2.ck \(\chi_{3675}(299, \cdot)\) n/a 3984 12
3675.2.cn \(\chi_{3675}(128, \cdot)\) n/a 6272 16
3675.2.cq \(\chi_{3675}(178, \cdot)\) n/a 3200 16
3675.2.cr \(\chi_{3675}(41, \cdot)\) n/a 13344 24
3675.2.ct \(\chi_{3675}(64, \cdot)\) n/a 6720 24
3675.2.cw \(\chi_{3675}(104, \cdot)\) n/a 13344 24
3675.2.cz \(\chi_{3675}(32, \cdot)\) n/a 7968 24
3675.2.da \(\chi_{3675}(82, \cdot)\) n/a 4032 24
3675.2.dc \(\chi_{3675}(16, \cdot)\) n/a 13440 48
3675.2.de \(\chi_{3675}(8, \cdot)\) n/a 26688 48
3675.2.df \(\chi_{3675}(13, \cdot)\) n/a 13440 48
3675.2.dj \(\chi_{3675}(59, \cdot)\) n/a 26688 48
3675.2.dk \(\chi_{3675}(4, \cdot)\) n/a 13440 48
3675.2.dm \(\chi_{3675}(131, \cdot)\) n/a 26688 48
3675.2.dp \(\chi_{3675}(52, \cdot)\) n/a 26880 96
3675.2.dq \(\chi_{3675}(2, \cdot)\) n/a 53376 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3675))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3675)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(525))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(735))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1225))\)\(^{\oplus 2}\)