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Properties

Label 2178.4
Level 2178
Weight 4
Dimension 101752
Nonzero newspaces 16
Sturm bound 1045440
Trace bound 2

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Defining parameters

Level: \( N \) = \( 2178 = 2 \cdot 3^{2} \cdot 11^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(1045440\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2178))\).

Total New Old
Modular forms 394600 101752 292848
Cusp forms 389480 101752 287728
Eisenstein series 5120 0 5120

Trace form

\( 101752 q + 4 q^{2} + 3 q^{3} - 8 q^{4} + 12 q^{5} - 18 q^{6} - 44 q^{7} - 8 q^{8} - 105 q^{9} + O(q^{10}) \) \( 101752 q + 4 q^{2} + 3 q^{3} - 8 q^{4} + 12 q^{5} - 18 q^{6} - 44 q^{7} - 8 q^{8} - 105 q^{9} + 188 q^{10} + 100 q^{11} + 24 q^{12} + 94 q^{13} + 28 q^{14} + 90 q^{15} - 32 q^{16} - 572 q^{17} + 156 q^{18} + 680 q^{19} + 48 q^{20} - 36 q^{21} + 3428 q^{23} + 776 q^{24} + 2932 q^{25} + 884 q^{26} - 240 q^{27} - 880 q^{28} - 4678 q^{29} - 3408 q^{30} - 5074 q^{31} - 896 q^{32} - 3200 q^{33} - 3258 q^{34} - 6952 q^{35} + 116 q^{36} - 994 q^{37} + 2 q^{38} + 618 q^{39} + 1392 q^{40} + 7691 q^{41} + 3824 q^{42} + 7177 q^{43} + 940 q^{44} + 4258 q^{45} - 552 q^{46} - 64 q^{47} - 144 q^{48} + 1988 q^{49} + 1796 q^{50} + 2747 q^{51} + 1976 q^{52} + 14370 q^{53} + 954 q^{54} + 3970 q^{55} + 272 q^{56} + 2107 q^{57} + 3552 q^{58} - 2457 q^{59} - 936 q^{60} - 7400 q^{61} - 4600 q^{62} - 11234 q^{63} + 448 q^{64} - 22134 q^{65} - 19329 q^{67} - 1820 q^{68} - 6986 q^{69} - 1272 q^{70} - 5824 q^{71} - 24 q^{72} + 260 q^{73} + 4164 q^{74} + 6731 q^{75} + 1180 q^{76} + 10090 q^{77} + 132 q^{78} + 16238 q^{79} + 608 q^{80} - 18965 q^{81} + 14500 q^{82} - 15936 q^{83} - 17176 q^{84} + 7952 q^{85} - 13210 q^{86} - 16804 q^{87} - 560 q^{88} - 2994 q^{89} + 9968 q^{90} - 25920 q^{91} + 8352 q^{92} + 24566 q^{93} - 8476 q^{94} + 29784 q^{95} + 384 q^{96} - 6487 q^{97} + 28890 q^{98} + 31360 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2178))\)

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
2178.4.a \(\chi_{2178}(1, \cdot)\) 2178.4.a.a 1 1
2178.4.a.b 1
2178.4.a.c 1
2178.4.a.d 1
2178.4.a.e 1
2178.4.a.f 1
2178.4.a.g 1
2178.4.a.h 1
2178.4.a.i 1
2178.4.a.j 1
2178.4.a.k 1
2178.4.a.l 1
2178.4.a.m 1
2178.4.a.n 1
2178.4.a.o 1
2178.4.a.p 1
2178.4.a.q 1
2178.4.a.r 1
2178.4.a.s 1
2178.4.a.t 1
2178.4.a.u 1
2178.4.a.v 1
2178.4.a.w 2
2178.4.a.x 2
2178.4.a.y 2
2178.4.a.z 2
2178.4.a.ba 2
2178.4.a.bb 2
2178.4.a.bc 2
2178.4.a.bd 2
2178.4.a.be 2
2178.4.a.bf 2
2178.4.a.bg 2
2178.4.a.bh 2
2178.4.a.bi 2
2178.4.a.bj 2
2178.4.a.bk 2
2178.4.a.bl 2
2178.4.a.bm 2
2178.4.a.bn 2
2178.4.a.bo 2
2178.4.a.bp 3
2178.4.a.bq 3
2178.4.a.br 3
2178.4.a.bs 3
2178.4.a.bt 4
2178.4.a.bu 4
2178.4.a.bv 4
2178.4.a.bw 4
2178.4.a.bx 4
2178.4.a.by 4
2178.4.a.bz 4
2178.4.a.ca 4
2178.4.a.cb 4
2178.4.a.cc 4
2178.4.a.cd 6
2178.4.a.ce 6
2178.4.a.cf 6
2178.4.a.cg 6
2178.4.b \(\chi_{2178}(2177, \cdot)\) n/a 108 1
2178.4.e \(\chi_{2178}(727, \cdot)\) n/a 654 2
2178.4.f \(\chi_{2178}(487, \cdot)\) n/a 540 4
2178.4.i \(\chi_{2178}(725, \cdot)\) n/a 648 2
2178.4.l \(\chi_{2178}(161, \cdot)\) n/a 432 4
2178.4.m \(\chi_{2178}(199, \cdot)\) n/a 1650 10
2178.4.n \(\chi_{2178}(493, \cdot)\) n/a 2592 8
2178.4.q \(\chi_{2178}(197, \cdot)\) n/a 1320 10
2178.4.r \(\chi_{2178}(239, \cdot)\) n/a 2592 8
2178.4.u \(\chi_{2178}(67, \cdot)\) n/a 7920 20
2178.4.v \(\chi_{2178}(37, \cdot)\) n/a 6600 40
2178.4.w \(\chi_{2178}(65, \cdot)\) n/a 7920 20
2178.4.z \(\chi_{2178}(17, \cdot)\) n/a 5280 40
2178.4.bc \(\chi_{2178}(25, \cdot)\) n/a 31680 80
2178.4.bf \(\chi_{2178}(29, \cdot)\) n/a 31680 80

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2178))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2178)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(726))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1089))\)\(^{\oplus 2}\)