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Properties

Label 1472.4
Level 1472
Weight 4
Dimension 113154
Nonzero newspaces 16
Sturm bound 540672
Trace bound 9

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Defining parameters

Level: \( N \) = \( 1472 = 2^{6} \cdot 23 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(540672\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1472))\).

Total New Old
Modular forms 204336 114078 90258
Cusp forms 201168 113154 88014
Eisenstein series 3168 924 2244

Trace form

\( 113154 q - 160 q^{2} - 120 q^{3} - 160 q^{4} - 160 q^{5} - 160 q^{6} - 116 q^{7} - 160 q^{8} - 146 q^{9} + O(q^{10}) \) \( 113154 q - 160 q^{2} - 120 q^{3} - 160 q^{4} - 160 q^{5} - 160 q^{6} - 116 q^{7} - 160 q^{8} - 146 q^{9} - 160 q^{10} - 80 q^{11} - 160 q^{12} - 304 q^{13} - 160 q^{14} - 364 q^{15} - 160 q^{16} - 488 q^{17} - 160 q^{18} - 168 q^{19} - 160 q^{20} - 136 q^{21} - 1104 q^{22} - 124 q^{23} - 2336 q^{24} - 302 q^{25} - 80 q^{26} + 252 q^{27} + 1360 q^{28} + 640 q^{29} + 4480 q^{30} + 604 q^{31} + 2320 q^{32} + 1844 q^{33} + 1840 q^{34} + 836 q^{35} + 1600 q^{36} + 880 q^{37} - 1040 q^{38} - 116 q^{39} - 3440 q^{40} - 2248 q^{41} - 6480 q^{42} - 1792 q^{43} - 2160 q^{44} - 3128 q^{45} - 168 q^{46} - 2136 q^{47} - 160 q^{48} - 2406 q^{49} + 5552 q^{50} - 9068 q^{51} + 6464 q^{52} - 976 q^{53} + 3296 q^{54} - 1268 q^{55} - 944 q^{56} + 1956 q^{57} - 4912 q^{58} + 8800 q^{59} - 9952 q^{60} + 2000 q^{61} - 6144 q^{62} + 15236 q^{63} - 12256 q^{64} + 4108 q^{65} - 11232 q^{66} + 11928 q^{67} - 4288 q^{68} + 468 q^{69} - 4368 q^{70} + 780 q^{71} + 1136 q^{72} - 2248 q^{73} + 5104 q^{74} - 14856 q^{75} + 11744 q^{76} - 6408 q^{77} + 3824 q^{78} - 20276 q^{79} - 8688 q^{80} - 13918 q^{81} - 14080 q^{82} - 5240 q^{83} - 8448 q^{84} - 3472 q^{85} + 880 q^{86} - 116 q^{87} + 6080 q^{88} + 6936 q^{89} + 18560 q^{90} + 6548 q^{91} + 12448 q^{92} + 16416 q^{93} + 17696 q^{94} + 13668 q^{95} + 25680 q^{96} + 18584 q^{97} + 24048 q^{98} + 9368 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1472))\)

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
1472.4.a \(\chi_{1472}(1, \cdot)\) 1472.4.a.a 1 1
1472.4.a.b 1
1472.4.a.c 1
1472.4.a.d 1
1472.4.a.e 1
1472.4.a.f 1
1472.4.a.g 1
1472.4.a.h 1
1472.4.a.i 1
1472.4.a.j 1
1472.4.a.k 2
1472.4.a.l 2
1472.4.a.m 2
1472.4.a.n 2
1472.4.a.o 3
1472.4.a.p 3
1472.4.a.q 3
1472.4.a.r 3
1472.4.a.s 3
1472.4.a.t 3
1472.4.a.u 3
1472.4.a.v 3
1472.4.a.w 3
1472.4.a.x 3
1472.4.a.y 4
1472.4.a.z 4
1472.4.a.ba 4
1472.4.a.bb 4
1472.4.a.bc 4
1472.4.a.bd 4
1472.4.a.be 4
1472.4.a.bf 4
1472.4.a.bg 8
1472.4.a.bh 8
1472.4.a.bi 9
1472.4.a.bj 9
1472.4.a.bk 9
1472.4.a.bl 9
1472.4.b \(\chi_{1472}(737, \cdot)\) n/a 132 1
1472.4.c \(\chi_{1472}(1471, \cdot)\) n/a 142 1
1472.4.h \(\chi_{1472}(735, \cdot)\) n/a 144 1
1472.4.i \(\chi_{1472}(367, \cdot)\) n/a 284 2
1472.4.j \(\chi_{1472}(369, \cdot)\) n/a 264 2
1472.4.m \(\chi_{1472}(185, \cdot)\) None 0 4
1472.4.n \(\chi_{1472}(183, \cdot)\) None 0 4
1472.4.q \(\chi_{1472}(193, \cdot)\) n/a 1420 10
1472.4.r \(\chi_{1472}(93, \cdot)\) n/a 4224 8
1472.4.u \(\chi_{1472}(91, \cdot)\) n/a 4592 8
1472.4.v \(\chi_{1472}(159, \cdot)\) n/a 1440 10
1472.4.ba \(\chi_{1472}(63, \cdot)\) n/a 1420 10
1472.4.bb \(\chi_{1472}(225, \cdot)\) n/a 1440 10
1472.4.be \(\chi_{1472}(49, \cdot)\) n/a 2840 20
1472.4.bf \(\chi_{1472}(15, \cdot)\) n/a 2840 20
1472.4.bi \(\chi_{1472}(7, \cdot)\) None 0 40
1472.4.bj \(\chi_{1472}(9, \cdot)\) None 0 40
1472.4.bk \(\chi_{1472}(11, \cdot)\) n/a 45920 80
1472.4.bn \(\chi_{1472}(13, \cdot)\) n/a 45920 80

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1472))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1472)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(736))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1472))\)\(^{\oplus 1}\)