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Properties

Label 344.6
Level 344
Weight 6
Dimension 10301
Nonzero newspaces 12
Sturm bound 44352
Trace bound 2

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Defining parameters

Level: \( N \) = \( 344 = 2^{3} \cdot 43 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(44352\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(344))\).

Total New Old
Modular forms 18732 10465 8267
Cusp forms 18228 10301 7927
Eisenstein series 504 164 340

Trace form

\( 10301 q - 38 q^{2} - 82 q^{3} - 82 q^{4} + 148 q^{5} + 190 q^{6} - 186 q^{7} + 454 q^{8} - 70 q^{9} + O(q^{10}) \) \( 10301 q - 38 q^{2} - 82 q^{3} - 82 q^{4} + 148 q^{5} + 190 q^{6} - 186 q^{7} + 454 q^{8} - 70 q^{9} - 1306 q^{10} - 290 q^{11} - 3194 q^{12} - 956 q^{13} + 4726 q^{14} + 3750 q^{15} + 6582 q^{16} + 1912 q^{17} - 9550 q^{18} - 6130 q^{19} - 9290 q^{20} + 960 q^{21} + 11230 q^{22} - 5082 q^{23} + 15542 q^{24} - 7898 q^{25} - 11258 q^{26} + 3398 q^{27} - 10346 q^{28} + 6564 q^{29} + 4214 q^{30} + 37270 q^{31} - 10858 q^{32} - 340 q^{33} + 9502 q^{34} - 3594 q^{35} + 20286 q^{36} - 20652 q^{37} - 32002 q^{38} - 89370 q^{39} - 32106 q^{40} + 26824 q^{41} + 52246 q^{42} + 9146 q^{43} + 58140 q^{44} + 23236 q^{45} - 58442 q^{46} + 62070 q^{47} - 71274 q^{48} + 12722 q^{49} + 94954 q^{50} + 47878 q^{51} + 73078 q^{52} - 23372 q^{53} - 46618 q^{54} - 152634 q^{55} - 81578 q^{56} - 117780 q^{57} - 7610 q^{58} - 33794 q^{59} - 5226 q^{60} + 36964 q^{61} - 69034 q^{62} + 314374 q^{63} + 83798 q^{64} + 109700 q^{65} - 86490 q^{66} + 31022 q^{67} - 20730 q^{68} - 734170 q^{69} + 137814 q^{70} - 421276 q^{71} + 166502 q^{72} + 159518 q^{73} - 34970 q^{74} + 916543 q^{75} - 199930 q^{76} + 605586 q^{77} + 348086 q^{78} + 490162 q^{79} + 70998 q^{80} - 406422 q^{81} - 322306 q^{82} - 631126 q^{83} - 393386 q^{84} - 784204 q^{85} + 18458 q^{86} - 1858158 q^{87} + 334390 q^{88} - 302828 q^{89} - 284602 q^{90} + 43986 q^{91} + 98070 q^{92} + 1087768 q^{93} + 197526 q^{94} + 1765858 q^{95} + 231254 q^{96} + 1582970 q^{97} + 234042 q^{98} + 1430287 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(344))\)

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
344.6.a \(\chi_{344}(1, \cdot)\) 344.6.a.a 11 1
344.6.a.b 13
344.6.a.c 14
344.6.a.d 15
344.6.c \(\chi_{344}(173, \cdot)\) n/a 210 1
344.6.e \(\chi_{344}(171, \cdot)\) n/a 218 1
344.6.g \(\chi_{344}(343, \cdot)\) None 0 1
344.6.i \(\chi_{344}(49, \cdot)\) n/a 110 2
344.6.k \(\chi_{344}(7, \cdot)\) None 0 2
344.6.m \(\chi_{344}(123, \cdot)\) n/a 436 2
344.6.o \(\chi_{344}(165, \cdot)\) n/a 436 2
344.6.q \(\chi_{344}(41, \cdot)\) n/a 330 6
344.6.t \(\chi_{344}(39, \cdot)\) None 0 6
344.6.v \(\chi_{344}(27, \cdot)\) n/a 1308 6
344.6.x \(\chi_{344}(21, \cdot)\) n/a 1308 6
344.6.y \(\chi_{344}(9, \cdot)\) n/a 660 12
344.6.z \(\chi_{344}(13, \cdot)\) n/a 2616 12
344.6.bb \(\chi_{344}(3, \cdot)\) n/a 2616 12
344.6.bd \(\chi_{344}(55, \cdot)\) None 0 12

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(344))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(344)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(86))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(172))\)\(^{\oplus 2}\)