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Properties

Label 3542.2
Level 3542
Weight 2
Dimension 118957
Nonzero newspaces 32
Sturm bound 1520640
Trace bound 5

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Defining parameters

Level: \( N \) = \( 3542 = 2 \cdot 7 \cdot 11 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(1520640\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3542))\).

Total New Old
Modular forms 385440 118957 266483
Cusp forms 374881 118957 255924
Eisenstein series 10559 0 10559

Trace form

\( 118957 q - 7 q^{2} - 20 q^{3} + q^{4} - 18 q^{5} + 16 q^{6} + 21 q^{7} - 7 q^{8} + 45 q^{9} + O(q^{10}) \) \( 118957 q - 7 q^{2} - 20 q^{3} + q^{4} - 18 q^{5} + 16 q^{6} + 21 q^{7} - 7 q^{8} + 45 q^{9} + 22 q^{10} + 17 q^{11} + 20 q^{12} - 18 q^{13} + 13 q^{14} + 136 q^{15} + q^{16} + 138 q^{17} + 153 q^{18} + 96 q^{19} + 70 q^{20} + 152 q^{21} + 21 q^{22} + 169 q^{23} + 16 q^{24} + 223 q^{25} + 142 q^{26} + 340 q^{27} + 65 q^{28} + 134 q^{29} + 224 q^{30} + 96 q^{31} + 13 q^{32} + 172 q^{33} + 2 q^{34} + 146 q^{35} - 15 q^{36} + 150 q^{37} + 52 q^{38} + 240 q^{39} + 22 q^{40} + 146 q^{41} + 56 q^{42} + 276 q^{43} + 37 q^{44} + 230 q^{45} - 7 q^{46} + 144 q^{47} - 20 q^{48} + 253 q^{49} + 7 q^{50} + 172 q^{51} + 22 q^{52} + 150 q^{53} + 112 q^{54} + 318 q^{55} + 37 q^{56} + 524 q^{57} + 270 q^{58} + 496 q^{59} + 96 q^{60} + 358 q^{61} + 184 q^{62} + 65 q^{63} + q^{64} + 404 q^{65} - 156 q^{66} + 76 q^{67} + 106 q^{68} + 172 q^{69} - 122 q^{70} + 64 q^{71} - 27 q^{72} - 158 q^{73} + 70 q^{74} - 128 q^{75} - 132 q^{76} - 113 q^{77} - 256 q^{78} + 72 q^{79} - 10 q^{80} - 299 q^{81} - 74 q^{82} - 24 q^{83} - 136 q^{84} - 100 q^{85} - 176 q^{86} - 248 q^{87} - 103 q^{88} - 126 q^{89} - 354 q^{90} - 130 q^{91} + 13 q^{92} - 192 q^{93} + 24 q^{94} + 224 q^{95} - 4 q^{96} + 398 q^{97} + 101 q^{98} + 573 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3542))\)

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
3542.2.a \(\chi_{3542}(1, \cdot)\) 3542.2.a.a 1 1
3542.2.a.b 1
3542.2.a.c 1
3542.2.a.d 1
3542.2.a.e 1
3542.2.a.f 1
3542.2.a.g 1
3542.2.a.h 1
3542.2.a.i 1
3542.2.a.j 1
3542.2.a.k 1
3542.2.a.l 1
3542.2.a.m 1
3542.2.a.n 1
3542.2.a.o 1
3542.2.a.p 1
3542.2.a.q 1
3542.2.a.r 1
3542.2.a.s 1
3542.2.a.t 2
3542.2.a.u 2
3542.2.a.v 2
3542.2.a.w 2
3542.2.a.x 4
3542.2.a.y 4
3542.2.a.z 4
3542.2.a.ba 5
3542.2.a.bb 5
3542.2.a.bc 7
3542.2.a.bd 8
3542.2.a.be 8
3542.2.a.bf 8
3542.2.a.bg 9
3542.2.a.bh 9
3542.2.a.bi 11
3542.2.c \(\chi_{3542}(461, \cdot)\) n/a 176 1
3542.2.d \(\chi_{3542}(2575, \cdot)\) n/a 160 1
3542.2.f \(\chi_{3542}(505, \cdot)\) n/a 144 1
3542.2.i \(\chi_{3542}(2025, \cdot)\) n/a 288 2
3542.2.j \(\chi_{3542}(323, \cdot)\) n/a 528 4
3542.2.l \(\chi_{3542}(2529, \cdot)\) n/a 384 2
3542.2.n \(\chi_{3542}(45, \cdot)\) n/a 320 2
3542.2.q \(\chi_{3542}(1473, \cdot)\) n/a 352 2
3542.2.t \(\chi_{3542}(183, \cdot)\) n/a 576 4
3542.2.v \(\chi_{3542}(643, \cdot)\) n/a 768 4
3542.2.w \(\chi_{3542}(139, \cdot)\) n/a 704 4
3542.2.y \(\chi_{3542}(463, \cdot)\) n/a 1200 10
3542.2.z \(\chi_{3542}(93, \cdot)\) n/a 1408 8
3542.2.bc \(\chi_{3542}(43, \cdot)\) n/a 1440 10
3542.2.be \(\chi_{3542}(111, \cdot)\) n/a 1600 10
3542.2.bf \(\chi_{3542}(307, \cdot)\) n/a 1920 10
3542.2.bh \(\chi_{3542}(369, \cdot)\) n/a 1408 8
3542.2.bk \(\chi_{3542}(229, \cdot)\) n/a 1536 8
3542.2.bm \(\chi_{3542}(459, \cdot)\) n/a 1536 8
3542.2.bo \(\chi_{3542}(177, \cdot)\) n/a 3200 20
3542.2.bp \(\chi_{3542}(71, \cdot)\) n/a 5760 40
3542.2.bq \(\chi_{3542}(87, \cdot)\) n/a 3840 20
3542.2.bt \(\chi_{3542}(89, \cdot)\) n/a 3200 20
3542.2.bv \(\chi_{3542}(65, \cdot)\) n/a 3840 20
3542.2.by \(\chi_{3542}(13, \cdot)\) n/a 7680 40
3542.2.bz \(\chi_{3542}(97, \cdot)\) n/a 7680 40
3542.2.cb \(\chi_{3542}(57, \cdot)\) n/a 5760 40
3542.2.ce \(\chi_{3542}(9, \cdot)\) n/a 15360 80
3542.2.cg \(\chi_{3542}(51, \cdot)\) n/a 15360 80
3542.2.ci \(\chi_{3542}(5, \cdot)\) n/a 15360 80
3542.2.cl \(\chi_{3542}(73, \cdot)\) n/a 15360 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3542))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3542)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(253))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(322))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(506))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1771))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3542))\)\(^{\oplus 1}\)