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Properties

Label 552.6
Level 552
Weight 6
Dimension 17670
Nonzero newspaces 12
Sturm bound 101376
Trace bound 4

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Defining parameters

Level: \( N \) = \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(101376\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(552))\).

Total New Old
Modular forms 42768 17838 24930
Cusp forms 41712 17670 24042
Eisenstein series 1056 168 888

Trace form

\( 17670 q - 4 q^{2} + 44 q^{4} - 196 q^{5} - 378 q^{6} + 300 q^{7} - 136 q^{8} + 1094 q^{9} + O(q^{10}) \) \( 17670 q - 4 q^{2} + 44 q^{4} - 196 q^{5} - 378 q^{6} + 300 q^{7} - 136 q^{8} + 1094 q^{9} + 1356 q^{10} - 40 q^{11} + 954 q^{12} + 204 q^{13} - 7384 q^{14} - 1426 q^{15} - 5740 q^{16} + 1340 q^{17} - 450 q^{18} + 15412 q^{19} + 12752 q^{20} - 3888 q^{21} - 12780 q^{22} - 6576 q^{23} - 436 q^{24} + 2030 q^{25} + 13040 q^{26} + 8904 q^{27} + 33780 q^{28} + 20844 q^{29} - 11998 q^{30} - 41268 q^{31} + 8176 q^{32} - 25188 q^{33} - 50564 q^{34} - 20612 q^{35} - 19662 q^{36} - 140908 q^{37} + 9424 q^{38} - 4270 q^{39} + 47364 q^{40} + 49992 q^{41} - 3358 q^{42} + 146124 q^{43} - 13824 q^{44} - 15876 q^{45} + 59788 q^{46} + 9224 q^{47} + 118650 q^{48} - 63658 q^{49} - 14788 q^{50} - 11414 q^{51} - 71180 q^{52} - 14232 q^{53} - 98802 q^{54} - 75812 q^{55} - 21616 q^{56} + 15072 q^{57} - 155028 q^{58} + 214548 q^{59} - 293878 q^{60} - 74196 q^{61} - 50600 q^{62} - 35662 q^{63} - 373516 q^{64} - 179864 q^{65} + 216760 q^{66} - 75164 q^{67} + 285312 q^{68} - 1800 q^{69} + 473976 q^{70} + 608992 q^{71} + 379218 q^{72} + 110812 q^{73} - 663188 q^{74} - 911694 q^{75} - 698664 q^{76} - 75840 q^{77} + 758758 q^{78} + 361032 q^{79} + 2392692 q^{80} + 919394 q^{81} + 1230292 q^{82} + 768580 q^{83} - 9546 q^{84} + 485124 q^{85} - 1498616 q^{86} - 871240 q^{87} - 2566636 q^{88} - 1321960 q^{89} - 2476412 q^{90} - 2102080 q^{91} - 2843100 q^{92} + 142272 q^{93} - 1260608 q^{94} - 1472632 q^{95} + 452600 q^{96} + 197656 q^{97} + 1764844 q^{98} + 1112044 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(552))\)

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
552.6.a \(\chi_{552}(1, \cdot)\) 552.6.a.a 1 1
552.6.a.b 5
552.6.a.c 6
552.6.a.d 6
552.6.a.e 6
552.6.a.f 7
552.6.a.g 7
552.6.a.h 8
552.6.a.i 8
552.6.b \(\chi_{552}(413, \cdot)\) n/a 476 1
552.6.e \(\chi_{552}(47, \cdot)\) None 0 1
552.6.f \(\chi_{552}(277, \cdot)\) n/a 220 1
552.6.i \(\chi_{552}(367, \cdot)\) None 0 1
552.6.j \(\chi_{552}(323, \cdot)\) n/a 440 1
552.6.m \(\chi_{552}(137, \cdot)\) n/a 120 1
552.6.n \(\chi_{552}(91, \cdot)\) n/a 240 1
552.6.q \(\chi_{552}(25, \cdot)\) n/a 600 10
552.6.t \(\chi_{552}(19, \cdot)\) n/a 2400 10
552.6.u \(\chi_{552}(17, \cdot)\) n/a 1200 10
552.6.x \(\chi_{552}(35, \cdot)\) n/a 4760 10
552.6.y \(\chi_{552}(7, \cdot)\) None 0 10
552.6.bb \(\chi_{552}(13, \cdot)\) n/a 2400 10
552.6.bc \(\chi_{552}(71, \cdot)\) None 0 10
552.6.bf \(\chi_{552}(5, \cdot)\) n/a 4760 10

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(552))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(552)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 2}\)