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Properties

Label 260.4
Level 260
Weight 4
Dimension 3128
Nonzero newspaces 20
Sturm bound 16128
Trace bound 7

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Defining parameters

Level: \( N \) = \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(16128\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(260))\).

Total New Old
Modular forms 6288 3256 3032
Cusp forms 5808 3128 2680
Eisenstein series 480 128 352

Trace form

\( 3128 q - 8 q^{2} - 8 q^{3} - 12 q^{4} - 66 q^{5} - 52 q^{6} + 104 q^{7} + 76 q^{8} + 194 q^{9} + O(q^{10}) \) \( 3128 q - 8 q^{2} - 8 q^{3} - 12 q^{4} - 66 q^{5} - 52 q^{6} + 104 q^{7} + 76 q^{8} + 194 q^{9} + 130 q^{10} - 80 q^{11} + 136 q^{12} - 440 q^{13} - 24 q^{14} - 416 q^{15} - 404 q^{16} + 22 q^{17} - 1740 q^{18} + 320 q^{19} - 770 q^{20} + 520 q^{21} + 48 q^{22} + 360 q^{23} + 2196 q^{24} - 202 q^{25} + 1924 q^{26} + 1960 q^{27} + 2888 q^{28} + 1962 q^{29} + 2702 q^{30} + 928 q^{31} + 232 q^{32} - 1480 q^{33} - 2268 q^{34} - 1096 q^{35} - 4556 q^{36} - 2834 q^{37} - 3224 q^{38} - 3920 q^{39} - 1764 q^{40} - 7514 q^{41} + 152 q^{42} - 976 q^{43} + 288 q^{44} + 799 q^{45} + 308 q^{46} + 1632 q^{47} + 1684 q^{48} + 7938 q^{49} + 1716 q^{50} + 4736 q^{51} - 3996 q^{52} + 4240 q^{53} - 4968 q^{54} - 428 q^{55} - 7480 q^{56} + 5216 q^{57} - 6300 q^{58} + 1720 q^{59} - 6068 q^{60} + 718 q^{61} - 7220 q^{62} - 4120 q^{63} - 335 q^{65} + 4320 q^{66} + 1760 q^{67} + 2816 q^{68} + 5776 q^{69} + 8324 q^{70} + 1920 q^{71} + 11664 q^{72} + 1128 q^{73} + 10908 q^{74} - 3736 q^{75} + 7364 q^{76} - 816 q^{77} + 13824 q^{78} + 1376 q^{79} + 3884 q^{80} - 9306 q^{81} + 5756 q^{82} + 2520 q^{83} + 9984 q^{84} - 7647 q^{85} + 15592 q^{86} - 5376 q^{87} + 8256 q^{88} + 2492 q^{89} + 4284 q^{90} - 7432 q^{91} - 10216 q^{92} - 10640 q^{93} - 15300 q^{94} - 5264 q^{95} - 21904 q^{96} + 12800 q^{97} - 12664 q^{98} + 8144 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(260))\)

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
260.4.a \(\chi_{260}(1, \cdot)\) 260.4.a.a 1 1
260.4.a.b 3
260.4.a.c 4
260.4.a.d 4
260.4.c \(\chi_{260}(209, \cdot)\) 260.4.c.a 2 1
260.4.c.b 16
260.4.d \(\chi_{260}(129, \cdot)\) 260.4.d.a 20 1
260.4.f \(\chi_{260}(181, \cdot)\) 260.4.f.a 14 1
260.4.i \(\chi_{260}(61, \cdot)\) 260.4.i.a 14 2
260.4.i.b 14
260.4.j \(\chi_{260}(31, \cdot)\) n/a 168 2
260.4.m \(\chi_{260}(57, \cdot)\) 260.4.m.a 2 2
260.4.m.b 40
260.4.o \(\chi_{260}(27, \cdot)\) n/a 216 2
260.4.p \(\chi_{260}(103, \cdot)\) n/a 244 2
260.4.r \(\chi_{260}(177, \cdot)\) 260.4.r.a 2 2
260.4.r.b 40
260.4.u \(\chi_{260}(99, \cdot)\) n/a 244 2
260.4.x \(\chi_{260}(101, \cdot)\) 260.4.x.a 28 2
260.4.z \(\chi_{260}(49, \cdot)\) 260.4.z.a 40 2
260.4.ba \(\chi_{260}(9, \cdot)\) 260.4.ba.a 44 2
260.4.bc \(\chi_{260}(19, \cdot)\) n/a 488 4
260.4.bf \(\chi_{260}(37, \cdot)\) 260.4.bf.a 84 4
260.4.bg \(\chi_{260}(23, \cdot)\) n/a 488 4
260.4.bj \(\chi_{260}(3, \cdot)\) n/a 488 4
260.4.bk \(\chi_{260}(33, \cdot)\) 260.4.bk.a 84 4
260.4.bn \(\chi_{260}(11, \cdot)\) n/a 336 4

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(260))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(260)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 2}\)