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Properties

Label 348.6
Level 348
Weight 6
Dimension 7278
Nonzero newspaces 12
Sturm bound 40320
Trace bound 6

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Defining parameters

Level: \( N \) = \( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(40320\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(348))\).

Total New Old
Modular forms 17080 7382 9698
Cusp forms 16520 7278 9242
Eisenstein series 560 104 456

Trace form

\( 7278 q - 44 q^{4} - 62 q^{6} + 20 q^{9} + O(q^{10}) \) \( 7278 q - 44 q^{4} - 62 q^{6} + 20 q^{9} + 516 q^{10} + 1378 q^{12} - 280 q^{13} - 4700 q^{16} - 7406 q^{18} - 6216 q^{21} + 16580 q^{22} - 15988 q^{23} + 22450 q^{24} + 4416 q^{25} + 27258 q^{27} - 38552 q^{28} + 42280 q^{29} - 50044 q^{30} + 11480 q^{31} - 40438 q^{33} + 72804 q^{34} - 85064 q^{35} + 84130 q^{36} - 42660 q^{37} + 56140 q^{39} - 107676 q^{40} - 118190 q^{42} - 229292 q^{44} - 11194 q^{45} + 130912 q^{46} + 105896 q^{47} + 463426 q^{48} + 369064 q^{49} + 480004 q^{50} + 90216 q^{51} - 40540 q^{52} - 65646 q^{53} - 156254 q^{54} - 533344 q^{55} - 581924 q^{56} - 268688 q^{57} - 1009628 q^{58} - 156184 q^{59} - 216854 q^{60} - 236808 q^{61} + 35476 q^{62} + 43092 q^{63} + 656488 q^{64} + 524034 q^{65} + 506818 q^{66} + 628432 q^{67} + 1062124 q^{68} + 427244 q^{69} + 515332 q^{70} - 95704 q^{71} - 242954 q^{72} - 777726 q^{73} - 695492 q^{74} + 487130 q^{75} + 172484 q^{76} + 167506 q^{78} - 525500 q^{81} - 309468 q^{82} - 332324 q^{84} - 458808 q^{85} - 511630 q^{87} + 300616 q^{88} + 502930 q^{90} + 839004 q^{93} - 772252 q^{94} + 831100 q^{96} - 2311514 q^{97} + 1142260 q^{98} + 867090 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(348))\)

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
348.6.a \(\chi_{348}(1, \cdot)\) 348.6.a.a 6 1
348.6.a.b 6
348.6.a.c 6
348.6.a.d 6
348.6.b \(\chi_{348}(347, \cdot)\) n/a 296 1
348.6.c \(\chi_{348}(59, \cdot)\) n/a 280 1
348.6.h \(\chi_{348}(289, \cdot)\) 348.6.h.a 26 1
348.6.i \(\chi_{348}(307, \cdot)\) n/a 300 2
348.6.l \(\chi_{348}(17, \cdot)\) 348.6.l.a 100 2
348.6.m \(\chi_{348}(25, \cdot)\) n/a 144 6
348.6.n \(\chi_{348}(13, \cdot)\) n/a 156 6
348.6.s \(\chi_{348}(23, \cdot)\) n/a 1776 6
348.6.t \(\chi_{348}(35, \cdot)\) n/a 1776 6
348.6.u \(\chi_{348}(77, \cdot)\) n/a 600 12
348.6.x \(\chi_{348}(19, \cdot)\) n/a 1800 12

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(348))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(348)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(174))\)\(^{\oplus 2}\)