Properties

Label 276.4
Level 276
Weight 4
Dimension 2718
Nonzero newspaces 8
Sturm bound 16896
Trace bound 1

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Defining parameters

Level: \( N \) = \( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(16896\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(276))\).

Total New Old
Modular forms 6556 2798 3758
Cusp forms 6116 2718 3398
Eisenstein series 440 80 360

Trace form

\( 2718 q - 6 q^{3} - 6 q^{4} + 36 q^{5} + 37 q^{6} - 16 q^{7} - 16 q^{9} + O(q^{10}) \) \( 2718 q - 6 q^{3} - 6 q^{4} + 36 q^{5} + 37 q^{6} - 16 q^{7} - 16 q^{9} - 182 q^{10} - 72 q^{11} - 251 q^{12} + 56 q^{13} + 482 q^{15} + 426 q^{16} + 140 q^{17} + 469 q^{18} - 20 q^{19} - 970 q^{21} - 524 q^{22} - 1040 q^{23} - 598 q^{24} - 1506 q^{25} - 120 q^{27} + 458 q^{28} + 908 q^{29} + 469 q^{30} + 1132 q^{31} + 1690 q^{33} - 4490 q^{34} - 2572 q^{35} - 1049 q^{36} - 928 q^{37} - 1210 q^{38} + 192 q^{39} + 1978 q^{40} + 920 q^{41} + 3139 q^{42} + 2528 q^{43} + 6622 q^{44} - 1640 q^{45} + 8570 q^{46} + 2920 q^{47} + 4381 q^{48} + 2606 q^{49} + 3850 q^{50} + 552 q^{51} + 478 q^{52} - 1312 q^{53} - 2189 q^{54} - 2664 q^{55} - 7150 q^{56} - 3202 q^{57} - 9512 q^{58} - 4660 q^{59} - 1721 q^{60} + 2648 q^{61} + 1946 q^{63} - 2838 q^{64} - 360 q^{65} - 2114 q^{66} - 664 q^{67} + 2158 q^{69} - 1004 q^{70} + 720 q^{71} + 1909 q^{72} - 3376 q^{73} + 4730 q^{74} - 3174 q^{75} + 12048 q^{76} - 21520 q^{77} + 9519 q^{78} - 3884 q^{79} + 8118 q^{80} - 876 q^{81} + 2086 q^{82} + 3212 q^{83} - 4921 q^{84} + 18256 q^{85} - 13420 q^{86} + 6090 q^{87} - 8166 q^{88} + 12480 q^{89} - 18044 q^{90} + 8168 q^{91} - 18018 q^{92} + 16588 q^{93} - 14340 q^{94} + 9204 q^{95} - 15618 q^{96} + 16628 q^{97} - 8624 q^{98} + 4434 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(276))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
276.4.a \(\chi_{276}(1, \cdot)\) 276.4.a.a 1 1
276.4.a.b 1
276.4.a.c 2
276.4.a.d 2
276.4.a.e 4
276.4.c \(\chi_{276}(47, \cdot)\) n/a 132 1
276.4.e \(\chi_{276}(91, \cdot)\) 276.4.e.a 72 1
276.4.g \(\chi_{276}(137, \cdot)\) 276.4.g.a 24 1
276.4.i \(\chi_{276}(13, \cdot)\) n/a 120 10
276.4.k \(\chi_{276}(5, \cdot)\) n/a 240 10
276.4.m \(\chi_{276}(7, \cdot)\) n/a 720 10
276.4.o \(\chi_{276}(35, \cdot)\) n/a 1400 10

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(276))\) into lower level spaces

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