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Properties

Label 1840.3
Level 1840
Weight 3
Dimension 103582
Nonzero newspaces 28
Sturm bound 608256
Trace bound 9

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Defining parameters

Level: \( N \) = \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 28 \)
Sturm bound: \(608256\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1840))\).

Total New Old
Modular forms 205216 104714 100502
Cusp forms 200288 103582 96706
Eisenstein series 4928 1132 3796

Trace form

\( 103582 q - 80 q^{2} - 62 q^{3} - 104 q^{4} - 161 q^{5} - 264 q^{6} - 70 q^{7} - 56 q^{8} + 14 q^{9} + O(q^{10}) \) \( 103582 q - 80 q^{2} - 62 q^{3} - 104 q^{4} - 161 q^{5} - 264 q^{6} - 70 q^{7} - 56 q^{8} + 14 q^{9} - 44 q^{10} - 246 q^{11} + 136 q^{12} - 106 q^{13} - 24 q^{14} - 183 q^{15} - 392 q^{16} - 330 q^{17} - 368 q^{18} + 70 q^{19} - 284 q^{20} - 306 q^{21} - 280 q^{22} + 108 q^{23} + 32 q^{24} + 39 q^{25} + 152 q^{26} + 430 q^{27} + 408 q^{28} + 242 q^{29} + 564 q^{30} - 46 q^{31} + 520 q^{32} + 242 q^{33} + 264 q^{34} - 191 q^{35} - 56 q^{36} - 26 q^{37} + 200 q^{38} - 818 q^{39} - 196 q^{40} - 114 q^{41} - 648 q^{42} - 638 q^{43} - 552 q^{44} - 712 q^{45} - 640 q^{46} - 600 q^{47} - 1320 q^{48} - 1114 q^{49} - 804 q^{50} - 126 q^{51} - 504 q^{52} + 70 q^{53} - 520 q^{54} + 125 q^{55} - 904 q^{56} - 182 q^{57} - 776 q^{58} + 774 q^{59} - 692 q^{60} - 194 q^{61} - 648 q^{62} + 1178 q^{63} - 536 q^{64} + 139 q^{65} - 1112 q^{66} + 866 q^{67} - 856 q^{68} + 146 q^{69} - 1576 q^{70} + 642 q^{71} - 1544 q^{72} - 58 q^{73} - 1320 q^{74} - 215 q^{75} - 1368 q^{76} - 1878 q^{77} - 648 q^{78} - 1650 q^{79} + 508 q^{80} - 3762 q^{81} + 1560 q^{82} - 1022 q^{83} + 2376 q^{84} - 1849 q^{85} + 1736 q^{86} - 2642 q^{87} + 1480 q^{88} - 926 q^{89} + 2204 q^{90} - 2088 q^{91} + 648 q^{92} - 820 q^{93} + 1800 q^{94} - 1571 q^{95} + 1624 q^{96} + 1126 q^{97} + 1664 q^{98} + 918 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1840))\)

We only show spaces with odd 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
1840.3.c \(\chi_{1840}(1151, \cdot)\) 1840.3.c.a 32 1
1840.3.c.b 56
1840.3.d \(\chi_{1840}(1241, \cdot)\) None 0 1
1840.3.g \(\chi_{1840}(689, \cdot)\) n/a 142 1
1840.3.h \(\chi_{1840}(599, \cdot)\) None 0 1
1840.3.k \(\chi_{1840}(321, \cdot)\) 1840.3.k.a 6 1
1840.3.k.b 10
1840.3.k.c 16
1840.3.k.d 16
1840.3.k.e 48
1840.3.l \(\chi_{1840}(231, \cdot)\) None 0 1
1840.3.o \(\chi_{1840}(1519, \cdot)\) n/a 132 1
1840.3.p \(\chi_{1840}(1609, \cdot)\) None 0 1
1840.3.q \(\chi_{1840}(93, \cdot)\) n/a 1056 2
1840.3.s \(\chi_{1840}(1563, \cdot)\) n/a 1144 2
1840.3.v \(\chi_{1840}(139, \cdot)\) n/a 1056 2
1840.3.w \(\chi_{1840}(229, \cdot)\) n/a 1144 2
1840.3.z \(\chi_{1840}(553, \cdot)\) None 0 2
1840.3.bb \(\chi_{1840}(183, \cdot)\) None 0 2
1840.3.bc \(\chi_{1840}(367, \cdot)\) n/a 288 2
1840.3.be \(\chi_{1840}(737, \cdot)\) n/a 264 2
1840.3.bh \(\chi_{1840}(781, \cdot)\) n/a 768 2
1840.3.bi \(\chi_{1840}(691, \cdot)\) n/a 704 2
1840.3.bl \(\chi_{1840}(643, \cdot)\) n/a 1144 2
1840.3.bn \(\chi_{1840}(1013, \cdot)\) n/a 1056 2
1840.3.bp \(\chi_{1840}(89, \cdot)\) None 0 10
1840.3.bq \(\chi_{1840}(239, \cdot)\) n/a 1440 10
1840.3.bt \(\chi_{1840}(71, \cdot)\) None 0 10
1840.3.bu \(\chi_{1840}(241, \cdot)\) n/a 960 10
1840.3.bx \(\chi_{1840}(39, \cdot)\) None 0 10
1840.3.by \(\chi_{1840}(129, \cdot)\) n/a 1420 10
1840.3.cb \(\chi_{1840}(201, \cdot)\) None 0 10
1840.3.cc \(\chi_{1840}(31, \cdot)\) n/a 960 10
1840.3.ce \(\chi_{1840}(77, \cdot)\) n/a 11440 20
1840.3.cg \(\chi_{1840}(83, \cdot)\) n/a 11440 20
1840.3.ci \(\chi_{1840}(131, \cdot)\) n/a 7680 20
1840.3.cl \(\chi_{1840}(21, \cdot)\) n/a 7680 20
1840.3.cn \(\chi_{1840}(177, \cdot)\) n/a 2840 20
1840.3.cp \(\chi_{1840}(63, \cdot)\) n/a 2880 20
1840.3.cq \(\chi_{1840}(7, \cdot)\) None 0 20
1840.3.cs \(\chi_{1840}(73, \cdot)\) None 0 20
1840.3.cu \(\chi_{1840}(109, \cdot)\) n/a 11440 20
1840.3.cx \(\chi_{1840}(59, \cdot)\) n/a 11440 20
1840.3.cz \(\chi_{1840}(43, \cdot)\) n/a 11440 20
1840.3.db \(\chi_{1840}(13, \cdot)\) n/a 11440 20

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1840))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1840)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(460))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(920))\)\(^{\oplus 2}\)