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Properties

Label 1148.4
Level 1148
Weight 4
Dimension 67148
Nonzero newspaces 32
Sturm bound 322560
Trace bound 9

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Defining parameters

Level: \( N \) = \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(322560\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1148))\).

Total New Old
Modular forms 122160 67924 54236
Cusp forms 119760 67148 52612
Eisenstein series 2400 776 1624

Trace form

\( 67148 q - 74 q^{2} + 12 q^{3} - 74 q^{4} - 172 q^{5} - 80 q^{6} - 48 q^{7} - 290 q^{8} - 232 q^{9} + O(q^{10}) \) \( 67148 q - 74 q^{2} + 12 q^{3} - 74 q^{4} - 172 q^{5} - 80 q^{6} - 48 q^{7} - 290 q^{8} - 232 q^{9} - 56 q^{10} + 168 q^{11} + 256 q^{12} + 140 q^{13} + 218 q^{14} + 384 q^{15} + 94 q^{16} - 280 q^{17} - 122 q^{18} - 636 q^{19} - 80 q^{20} - 1484 q^{21} - 452 q^{22} - 168 q^{23} - 776 q^{24} + 944 q^{25} - 872 q^{26} + 1224 q^{27} - 1390 q^{28} + 1400 q^{29} - 1880 q^{30} + 1328 q^{31} - 1754 q^{32} - 40 q^{33} - 80 q^{34} - 1396 q^{35} + 1822 q^{36} - 4600 q^{37} + 3160 q^{38} - 5072 q^{39} + 2976 q^{40} - 680 q^{41} + 3808 q^{42} - 472 q^{43} + 4084 q^{44} - 1332 q^{45} + 2236 q^{46} + 816 q^{47} - 80 q^{48} + 384 q^{49} - 3098 q^{50} + 6888 q^{51} - 5264 q^{52} + 2224 q^{53} - 9224 q^{54} - 3744 q^{55} - 7174 q^{56} - 3832 q^{57} - 5108 q^{58} - 1740 q^{59} - 4496 q^{60} + 380 q^{61} - 80 q^{62} + 1896 q^{63} + 3334 q^{64} - 4628 q^{65} - 16976 q^{66} - 14136 q^{67} - 8112 q^{68} - 13096 q^{69} + 4388 q^{70} - 5648 q^{71} + 8662 q^{72} + 2696 q^{73} + 9748 q^{74} + 16116 q^{75} + 30520 q^{76} + 11064 q^{77} + 20152 q^{78} + 14184 q^{79} + 17456 q^{80} + 28644 q^{81} + 31108 q^{82} + 8980 q^{83} - 3436 q^{84} + 19724 q^{85} + 9620 q^{86} + 9096 q^{87} + 8380 q^{88} + 14376 q^{89} + 5320 q^{90} + 2580 q^{91} - 428 q^{92} + 3872 q^{93} - 13520 q^{94} - 14312 q^{95} - 28112 q^{96} - 27520 q^{97} + 318 q^{98} - 22704 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1148))\)

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
1148.4.a \(\chi_{1148}(1, \cdot)\) 1148.4.a.a 15 1
1148.4.a.b 15
1148.4.a.c 15
1148.4.a.d 15
1148.4.c \(\chi_{1148}(1147, \cdot)\) n/a 500 1
1148.4.d \(\chi_{1148}(1065, \cdot)\) 1148.4.d.a 64 1
1148.4.f \(\chi_{1148}(83, \cdot)\) n/a 480 1
1148.4.i \(\chi_{1148}(165, \cdot)\) n/a 160 2
1148.4.k \(\chi_{1148}(337, \cdot)\) n/a 124 2
1148.4.l \(\chi_{1148}(419, \cdot)\) n/a 1000 2
1148.4.n \(\chi_{1148}(57, \cdot)\) n/a 256 4
1148.4.p \(\chi_{1148}(411, \cdot)\) n/a 960 2
1148.4.r \(\chi_{1148}(81, \cdot)\) n/a 168 2
1148.4.u \(\chi_{1148}(327, \cdot)\) n/a 1000 2
1148.4.w \(\chi_{1148}(489, \cdot)\) n/a 336 4
1148.4.y \(\chi_{1148}(407, \cdot)\) n/a 1512 4
1148.4.ba \(\chi_{1148}(113, \cdot)\) n/a 256 4
1148.4.bb \(\chi_{1148}(195, \cdot)\) n/a 2000 4
1148.4.bf \(\chi_{1148}(139, \cdot)\) n/a 2000 4
1148.4.bh \(\chi_{1148}(255, \cdot)\) n/a 2000 4
1148.4.bi \(\chi_{1148}(9, \cdot)\) n/a 336 4
1148.4.bk \(\chi_{1148}(37, \cdot)\) n/a 672 8
1148.4.bm \(\chi_{1148}(251, \cdot)\) n/a 4000 8
1148.4.bn \(\chi_{1148}(169, \cdot)\) n/a 496 8
1148.4.bp \(\chi_{1148}(79, \cdot)\) n/a 4000 8
1148.4.br \(\chi_{1148}(325, \cdot)\) n/a 672 8
1148.4.bu \(\chi_{1148}(59, \cdot)\) n/a 4000 8
1148.4.bw \(\chi_{1148}(31, \cdot)\) n/a 4000 8
1148.4.bz \(\chi_{1148}(25, \cdot)\) n/a 672 8
1148.4.ca \(\chi_{1148}(15, \cdot)\) n/a 6048 16
1148.4.cc \(\chi_{1148}(13, \cdot)\) n/a 1344 16
1148.4.cf \(\chi_{1148}(121, \cdot)\) n/a 1344 16
1148.4.cg \(\chi_{1148}(87, \cdot)\) n/a 8000 16
1148.4.cj \(\chi_{1148}(17, \cdot)\) n/a 2688 32
1148.4.cl \(\chi_{1148}(11, \cdot)\) n/a 16000 32

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1148))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1148)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(287))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(574))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1148))\)\(^{\oplus 1}\)