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Properties

Label 612.4
Level 612
Weight 4
Dimension 14130
Nonzero newspaces 20
Sturm bound 82944
Trace bound 9

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Defining parameters

Level: \( N \) = \( 612 = 2^{2} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(82944\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(612))\).

Total New Old
Modular forms 31744 14402 17342
Cusp forms 30464 14130 16334
Eisenstein series 1280 272 1008

Trace form

\( 14130 q - 18 q^{2} + 6 q^{3} - 46 q^{4} - 84 q^{5} - 74 q^{6} - 4 q^{7} - 24 q^{8} - 154 q^{9} + O(q^{10}) \) \( 14130 q - 18 q^{2} + 6 q^{3} - 46 q^{4} - 84 q^{5} - 74 q^{6} - 4 q^{7} - 24 q^{8} - 154 q^{9} + 232 q^{10} - 142 q^{11} - 20 q^{12} - 160 q^{13} + 132 q^{14} + 360 q^{15} - 542 q^{16} + 320 q^{17} + 176 q^{18} + 220 q^{19} + 444 q^{20} + 428 q^{21} + 906 q^{22} - 484 q^{23} - 38 q^{24} + 132 q^{25} + 712 q^{26} - 1296 q^{27} - 912 q^{28} - 1844 q^{29} - 908 q^{30} - 928 q^{31} - 2638 q^{32} + 1934 q^{33} - 2125 q^{34} + 928 q^{35} - 2078 q^{36} - 1428 q^{37} - 2326 q^{38} + 2696 q^{39} + 52 q^{40} + 1990 q^{41} - 1496 q^{42} + 494 q^{43} + 2440 q^{44} - 3720 q^{45} + 840 q^{46} - 4740 q^{47} + 2710 q^{48} - 472 q^{49} + 3906 q^{50} - 1553 q^{51} + 5128 q^{52} + 2688 q^{53} + 6010 q^{54} + 272 q^{55} + 3388 q^{56} - 218 q^{57} - 1140 q^{58} - 82 q^{59} + 2572 q^{60} - 4524 q^{61} + 2048 q^{62} + 1296 q^{63} + 3572 q^{64} - 2196 q^{65} - 6388 q^{66} - 1310 q^{67} + 1027 q^{68} - 152 q^{69} - 1480 q^{70} - 3408 q^{71} - 10982 q^{72} - 2676 q^{73} - 10572 q^{74} - 1842 q^{75} + 686 q^{76} - 1684 q^{77} - 5000 q^{78} + 640 q^{79} - 8008 q^{80} - 3730 q^{81} - 6508 q^{82} - 2200 q^{83} - 4732 q^{84} - 12896 q^{85} - 16746 q^{86} - 7692 q^{87} - 10878 q^{88} - 5844 q^{89} + 14932 q^{90} + 976 q^{91} + 21120 q^{92} + 7200 q^{93} + 19320 q^{94} + 21296 q^{95} + 29352 q^{96} + 19506 q^{97} + 36288 q^{98} + 17388 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(612))\)

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
612.4.a \(\chi_{612}(1, \cdot)\) 612.4.a.a 1 1
612.4.a.b 1
612.4.a.c 1
612.4.a.d 1
612.4.a.e 2
612.4.a.f 2
612.4.a.g 3
612.4.a.h 3
612.4.a.i 3
612.4.a.j 3
612.4.b \(\chi_{612}(577, \cdot)\) 612.4.b.a 4 1
612.4.b.b 4
612.4.b.c 4
612.4.b.d 10
612.4.c \(\chi_{612}(35, \cdot)\) 612.4.c.a 96 1
612.4.h \(\chi_{612}(611, \cdot)\) n/a 108 1
612.4.i \(\chi_{612}(205, \cdot)\) 612.4.i.a 44 2
612.4.i.b 52
612.4.k \(\chi_{612}(217, \cdot)\) 612.4.k.a 2 2
612.4.k.b 6
612.4.k.c 16
612.4.k.d 20
612.4.m \(\chi_{612}(251, \cdot)\) n/a 216 2
612.4.n \(\chi_{612}(203, \cdot)\) n/a 640 2
612.4.s \(\chi_{612}(239, \cdot)\) n/a 576 2
612.4.t \(\chi_{612}(169, \cdot)\) n/a 108 2
612.4.w \(\chi_{612}(145, \cdot)\) 612.4.w.a 20 4
612.4.w.b 32
612.4.w.c 40
612.4.x \(\chi_{612}(179, \cdot)\) n/a 432 4
612.4.z \(\chi_{612}(13, \cdot)\) n/a 216 4
612.4.bb \(\chi_{612}(47, \cdot)\) n/a 1280 4
612.4.bc \(\chi_{612}(125, \cdot)\) n/a 144 8
612.4.bd \(\chi_{612}(91, \cdot)\) n/a 1064 8
612.4.bi \(\chi_{612}(25, \cdot)\) n/a 432 8
612.4.bj \(\chi_{612}(59, \cdot)\) n/a 2560 8
612.4.bk \(\chi_{612}(7, \cdot)\) n/a 5120 16
612.4.bl \(\chi_{612}(5, \cdot)\) n/a 864 16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(612))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(612)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(306))\)\(^{\oplus 2}\)