Properties

Label 735.3
Level 735
Weight 3
Dimension 24536
Nonzero newspaces 24
Sturm bound 112896
Trace bound 4

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Defining parameters

Level: \( N \) = \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(112896\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(735))\).

Total New Old
Modular forms 38592 25116 13476
Cusp forms 36672 24536 12136
Eisenstein series 1920 580 1340

Trace form

\( 24536 q - 4 q^{2} - 46 q^{3} - 132 q^{4} - 16 q^{5} - 110 q^{6} - 56 q^{7} - 12 q^{8} - 98 q^{9} + O(q^{10}) \) \( 24536 q - 4 q^{2} - 46 q^{3} - 132 q^{4} - 16 q^{5} - 110 q^{6} - 56 q^{7} - 12 q^{8} - 98 q^{9} - 78 q^{10} + 40 q^{11} + 82 q^{12} - 28 q^{13} + 48 q^{14} + 11 q^{15} + 156 q^{16} + 152 q^{17} + 314 q^{18} - 76 q^{19} - 36 q^{20} - 150 q^{21} - 452 q^{22} - 328 q^{23} - 162 q^{24} + 146 q^{25} + 352 q^{26} + 2 q^{27} + 312 q^{28} + 432 q^{29} + 541 q^{30} + 428 q^{31} + 812 q^{32} + 790 q^{33} + 964 q^{34} + 138 q^{35} + 230 q^{36} + 1436 q^{37} + 1512 q^{38} + 464 q^{39} + 410 q^{40} + 448 q^{41} + 258 q^{42} - 812 q^{43} - 576 q^{44} - 1025 q^{45} - 1124 q^{46} - 1216 q^{47} - 1556 q^{48} - 636 q^{49} - 100 q^{50} - 1118 q^{51} - 1236 q^{52} - 832 q^{53} - 338 q^{54} - 36 q^{55} - 2748 q^{56} + 734 q^{57} + 676 q^{58} + 408 q^{59} + 817 q^{60} - 120 q^{61} + 760 q^{62} + 60 q^{63} + 324 q^{64} + 1076 q^{65} + 626 q^{66} + 988 q^{67} + 568 q^{68} + 894 q^{69} - 522 q^{70} - 176 q^{71} - 6 q^{72} - 2044 q^{73} - 2280 q^{74} - 787 q^{75} - 4908 q^{76} - 1008 q^{77} - 950 q^{78} - 2756 q^{79} - 2350 q^{80} + 2578 q^{81} + 864 q^{82} + 2000 q^{83} + 4308 q^{84} - 1458 q^{85} + 3820 q^{86} + 1358 q^{87} + 5184 q^{88} + 2448 q^{89} - 214 q^{90} + 1516 q^{91} + 2708 q^{92} - 906 q^{93} + 688 q^{94} - 60 q^{95} - 4180 q^{96} - 1808 q^{97} - 1716 q^{98} - 3352 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(735))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
735.3.c \(\chi_{735}(491, \cdot)\) n/a 110 1
735.3.e \(\chi_{735}(244, \cdot)\) 735.3.e.a 32 1
735.3.e.b 48
735.3.f \(\chi_{735}(344, \cdot)\) n/a 154 1
735.3.h \(\chi_{735}(391, \cdot)\) 735.3.h.a 8 1
735.3.h.b 12
735.3.h.c 32
735.3.k \(\chi_{735}(293, \cdot)\) n/a 304 2
735.3.l \(\chi_{735}(148, \cdot)\) n/a 164 2
735.3.n \(\chi_{735}(31, \cdot)\) n/a 108 2
735.3.o \(\chi_{735}(569, \cdot)\) n/a 304 2
735.3.r \(\chi_{735}(19, \cdot)\) n/a 160 2
735.3.t \(\chi_{735}(116, \cdot)\) n/a 212 2
735.3.w \(\chi_{735}(67, \cdot)\) n/a 320 4
735.3.x \(\chi_{735}(68, \cdot)\) n/a 608 4
735.3.z \(\chi_{735}(76, \cdot)\) n/a 456 6
735.3.bb \(\chi_{735}(29, \cdot)\) n/a 1320 6
735.3.bc \(\chi_{735}(34, \cdot)\) n/a 672 6
735.3.be \(\chi_{735}(71, \cdot)\) n/a 888 6
735.3.bh \(\chi_{735}(22, \cdot)\) n/a 1344 12
735.3.bk \(\chi_{735}(62, \cdot)\) n/a 2640 12
735.3.bl \(\chi_{735}(11, \cdot)\) n/a 1800 12
735.3.bn \(\chi_{735}(94, \cdot)\) n/a 1344 12
735.3.bq \(\chi_{735}(44, \cdot)\) n/a 2640 12
735.3.br \(\chi_{735}(61, \cdot)\) n/a 888 12
735.3.bs \(\chi_{735}(17, \cdot)\) n/a 5280 24
735.3.bv \(\chi_{735}(37, \cdot)\) n/a 2688 24

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(735))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(735)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 2}\)