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Properties

Label 342.7
Level 342
Weight 7
Dimension 5102
Nonzero newspaces 16
Sturm bound 45360
Trace bound 4

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Defining parameters

Level: \( N \) = \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(45360\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(342))\).

Total New Old
Modular forms 19728 5102 14626
Cusp forms 19152 5102 14050
Eisenstein series 576 0 576

Trace form

\( 5102 q + 84 q^{3} - 256 q^{4} - 864 q^{5} + 288 q^{6} + 1456 q^{7} - 4380 q^{9} + O(q^{10}) \) \( 5102 q + 84 q^{3} - 256 q^{4} - 864 q^{5} + 288 q^{6} + 1456 q^{7} - 4380 q^{9} + 3936 q^{10} - 756 q^{11} - 768 q^{12} + 3328 q^{13} + 13248 q^{14} + 21744 q^{15} + 8192 q^{16} - 14400 q^{17} + 5952 q^{18} + 33668 q^{19} + 4608 q^{20} - 49752 q^{21} + 69936 q^{22} + 144576 q^{23} + 12288 q^{24} - 114904 q^{25} - 76608 q^{26} - 254016 q^{27} - 23552 q^{28} - 78264 q^{29} - 68544 q^{30} + 147004 q^{31} + 492516 q^{33} + 55008 q^{34} - 225432 q^{35} - 76416 q^{36} - 159032 q^{37} - 97632 q^{38} - 84408 q^{39} - 125952 q^{40} + 1013724 q^{41} + 444288 q^{42} + 1161916 q^{43} + 388800 q^{44} - 1291464 q^{45} - 2022432 q^{46} - 4060764 q^{47} - 294912 q^{48} - 256080 q^{49} + 1446336 q^{50} + 2322396 q^{51} + 901504 q^{52} + 4276800 q^{53} + 2053440 q^{54} + 1684944 q^{55} + 304128 q^{56} - 1191318 q^{57} - 1637184 q^{58} - 7543476 q^{59} - 1737216 q^{60} - 6614948 q^{61} - 3790800 q^{62} - 1768080 q^{63} + 917504 q^{64} + 6538500 q^{65} + 2979648 q^{66} + 5773156 q^{67} - 12096 q^{68} + 1216656 q^{69} + 450240 q^{70} - 5270760 q^{71} - 1370112 q^{72} - 4416986 q^{73} + 4394304 q^{74} + 4230684 q^{75} + 412736 q^{76} - 2847636 q^{77} + 1262976 q^{78} + 4955200 q^{79} + 2856564 q^{81} - 252384 q^{82} + 2601576 q^{83} - 2883072 q^{84} - 3681288 q^{85} - 7758432 q^{86} - 6145272 q^{87} - 1201152 q^{88} - 6096204 q^{89} + 3974400 q^{90} + 56192 q^{91} + 3156480 q^{92} + 5053152 q^{93} + 3211296 q^{94} + 20892708 q^{95} + 98304 q^{96} - 4232684 q^{97} + 6565248 q^{98} - 26079516 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(342))\)

We only show spaces with odd 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
342.7.c \(\chi_{342}(305, \cdot)\) 342.7.c.a 16 1
342.7.c.b 20
342.7.d \(\chi_{342}(37, \cdot)\) 342.7.d.a 10 1
342.7.d.b 20
342.7.d.c 20
342.7.i \(\chi_{342}(11, \cdot)\) n/a 240 2
342.7.k \(\chi_{342}(103, \cdot)\) n/a 240 2
342.7.l \(\chi_{342}(151, \cdot)\) n/a 240 2
342.7.m \(\chi_{342}(145, \cdot)\) 342.7.m.a 20 2
342.7.m.b 20
342.7.m.c 20
342.7.m.d 40
342.7.o \(\chi_{342}(77, \cdot)\) n/a 216 2
342.7.q \(\chi_{342}(83, \cdot)\) n/a 240 2
342.7.r \(\chi_{342}(125, \cdot)\) 342.7.r.a 40 2
342.7.r.b 40
342.7.t \(\chi_{342}(31, \cdot)\) n/a 240 2
342.7.y \(\chi_{342}(5, \cdot)\) n/a 720 6
342.7.z \(\chi_{342}(91, \cdot)\) n/a 300 6
342.7.ba \(\chi_{342}(17, \cdot)\) n/a 240 6
342.7.bc \(\chi_{342}(193, \cdot)\) n/a 720 6
342.7.bd \(\chi_{342}(13, \cdot)\) n/a 720 6
342.7.be \(\chi_{342}(23, \cdot)\) n/a 720 6

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

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(342))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(342)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(342))\)\(^{\oplus 1}\)