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Properties

Label 3630.2
Level 3630
Weight 2
Dimension 78548
Nonzero newspaces 24
Sturm bound 1393920
Trace bound 4

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Defining parameters

Level: \( N \) = \( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(1393920\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3630))\).

Total New Old
Modular forms 353600 78548 275052
Cusp forms 343361 78548 264813
Eisenstein series 10239 0 10239

Trace form

\( 78548 q - 2 q^{3} - 4 q^{5} - 22 q^{6} - 80 q^{7} - 80 q^{9} + O(q^{10}) \) \( 78548 q - 2 q^{3} - 4 q^{5} - 22 q^{6} - 80 q^{7} - 80 q^{9} - 36 q^{10} - 40 q^{11} - 34 q^{12} - 64 q^{13} - 64 q^{14} - 50 q^{15} - 136 q^{17} - 12 q^{18} - 104 q^{19} + 4 q^{20} - 72 q^{21} - 56 q^{23} + 18 q^{24} - 88 q^{25} + 118 q^{27} - 56 q^{29} + 46 q^{30} - 64 q^{31} + 90 q^{33} + 16 q^{34} - 24 q^{35} + 20 q^{36} + 64 q^{37} + 24 q^{38} + 68 q^{39} + 12 q^{40} - 40 q^{41} + 136 q^{42} + 144 q^{43} + 40 q^{44} - 4 q^{45} + 208 q^{46} + 208 q^{47} + 6 q^{48} + 392 q^{49} + 248 q^{50} + 112 q^{51} + 176 q^{52} + 288 q^{53} + 38 q^{54} + 220 q^{55} + 8 q^{56} + 300 q^{57} + 336 q^{58} + 280 q^{59} + 114 q^{60} + 272 q^{61} + 104 q^{62} + 120 q^{63} + 240 q^{65} - 40 q^{66} + 128 q^{67} + 24 q^{68} + 56 q^{69} - 224 q^{71} - 88 q^{72} - 264 q^{73} - 120 q^{74} - 118 q^{75} - 48 q^{76} - 160 q^{77} - 148 q^{78} - 152 q^{79} - 44 q^{80} - 128 q^{81} - 8 q^{82} - 144 q^{83} + 8 q^{84} - 96 q^{85} - 184 q^{86} + 44 q^{87} - 40 q^{88} - 112 q^{89} + 32 q^{90} + 448 q^{91} + 24 q^{92} + 168 q^{93} + 192 q^{94} + 224 q^{95} + 6 q^{96} + 472 q^{97} + 48 q^{98} + 260 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3630))\)

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
3630.2.a \(\chi_{3630}(1, \cdot)\) 3630.2.a.a 1 1
3630.2.a.b 1
3630.2.a.c 1
3630.2.a.d 1
3630.2.a.e 1
3630.2.a.f 1
3630.2.a.g 1
3630.2.a.h 1
3630.2.a.i 1
3630.2.a.j 1
3630.2.a.k 1
3630.2.a.l 1
3630.2.a.m 1
3630.2.a.n 1
3630.2.a.o 1
3630.2.a.p 1
3630.2.a.q 1
3630.2.a.r 1
3630.2.a.s 1
3630.2.a.t 1
3630.2.a.u 1
3630.2.a.v 1
3630.2.a.w 1
3630.2.a.x 1
3630.2.a.y 1
3630.2.a.z 1
3630.2.a.ba 2
3630.2.a.bb 2
3630.2.a.bc 2
3630.2.a.bd 2
3630.2.a.be 2
3630.2.a.bf 2
3630.2.a.bg 2
3630.2.a.bh 2
3630.2.a.bi 2
3630.2.a.bj 2
3630.2.a.bk 2
3630.2.a.bl 2
3630.2.a.bm 2
3630.2.a.bn 2
3630.2.a.bo 2
3630.2.a.bp 2
3630.2.a.bq 4
3630.2.a.br 4
3630.2.a.bs 4
3630.2.a.bt 4
3630.2.c \(\chi_{3630}(2179, \cdot)\) n/a 110 1
3630.2.d \(\chi_{3630}(1451, \cdot)\) n/a 144 1
3630.2.f \(\chi_{3630}(3629, \cdot)\) n/a 216 1
3630.2.j \(\chi_{3630}(1937, \cdot)\) n/a 436 2
3630.2.l \(\chi_{3630}(967, \cdot)\) n/a 216 2
3630.2.m \(\chi_{3630}(511, \cdot)\) n/a 288 4
3630.2.p \(\chi_{3630}(239, \cdot)\) n/a 864 4
3630.2.r \(\chi_{3630}(161, \cdot)\) n/a 576 4
3630.2.s \(\chi_{3630}(1219, \cdot)\) n/a 432 4
3630.2.u \(\chi_{3630}(331, \cdot)\) n/a 880 10
3630.2.v \(\chi_{3630}(403, \cdot)\) n/a 864 8
3630.2.x \(\chi_{3630}(323, \cdot)\) n/a 1728 8
3630.2.bb \(\chi_{3630}(329, \cdot)\) n/a 2640 10
3630.2.bd \(\chi_{3630}(131, \cdot)\) n/a 1760 10
3630.2.be \(\chi_{3630}(199, \cdot)\) n/a 1320 10
3630.2.bg \(\chi_{3630}(43, \cdot)\) n/a 2640 20
3630.2.bi \(\chi_{3630}(23, \cdot)\) n/a 5280 20
3630.2.bk \(\chi_{3630}(31, \cdot)\) n/a 3520 40
3630.2.bm \(\chi_{3630}(49, \cdot)\) n/a 5280 40
3630.2.bn \(\chi_{3630}(41, \cdot)\) n/a 7040 40
3630.2.bp \(\chi_{3630}(29, \cdot)\) n/a 10560 40
3630.2.bt \(\chi_{3630}(47, \cdot)\) n/a 21120 80
3630.2.bv \(\chi_{3630}(7, \cdot)\) n/a 10560 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3630))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3630)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(726))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1815))\)\(^{\oplus 2}\)