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Properties

Label 1472.2
Level 1472
Weight 2
Dimension 37410
Nonzero newspaces 16
Sturm bound 270336
Trace bound 9

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Defining parameters

Level: \( N \) = \( 1472 = 2^{6} \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(270336\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1472))\).

Total New Old
Modular forms 69168 38334 30834
Cusp forms 66001 37410 28591
Eisenstein series 3167 924 2243

Trace form

\( 37410 q - 160 q^{2} - 120 q^{3} - 160 q^{4} - 160 q^{5} - 160 q^{6} - 116 q^{7} - 160 q^{8} - 194 q^{9} + O(q^{10}) \) \( 37410 q - 160 q^{2} - 120 q^{3} - 160 q^{4} - 160 q^{5} - 160 q^{6} - 116 q^{7} - 160 q^{8} - 194 q^{9} - 160 q^{10} - 112 q^{11} - 160 q^{12} - 144 q^{13} - 160 q^{14} - 108 q^{15} - 160 q^{16} - 264 q^{17} - 160 q^{18} - 104 q^{19} - 160 q^{20} - 168 q^{21} - 176 q^{22} - 124 q^{23} - 416 q^{24} - 222 q^{25} - 240 q^{26} - 132 q^{27} - 240 q^{28} - 192 q^{29} - 320 q^{30} - 164 q^{31} - 240 q^{32} - 172 q^{33} - 240 q^{34} - 124 q^{35} - 320 q^{36} - 176 q^{37} - 240 q^{38} - 116 q^{39} - 240 q^{40} - 200 q^{41} - 240 q^{42} - 96 q^{43} - 176 q^{44} - 152 q^{45} - 168 q^{46} - 216 q^{47} - 160 q^{48} - 262 q^{49} - 112 q^{50} - 172 q^{51} - 64 q^{52} - 112 q^{53} - 32 q^{54} - 244 q^{55} - 48 q^{56} - 188 q^{57} - 16 q^{58} - 256 q^{59} + 32 q^{60} - 144 q^{61} - 96 q^{62} - 252 q^{63} + 32 q^{64} - 436 q^{65} - 296 q^{67} - 64 q^{68} - 156 q^{69} - 144 q^{70} - 244 q^{71} - 16 q^{72} - 200 q^{73} - 48 q^{74} - 232 q^{75} - 32 q^{76} - 168 q^{77} - 112 q^{78} - 180 q^{79} - 240 q^{80} - 286 q^{81} - 320 q^{82} - 120 q^{83} - 384 q^{84} - 176 q^{85} - 368 q^{86} - 116 q^{87} - 320 q^{88} - 296 q^{89} - 448 q^{90} - 108 q^{91} - 320 q^{92} - 416 q^{93} - 352 q^{94} - 156 q^{95} - 432 q^{96} - 200 q^{97} - 432 q^{98} - 168 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1472))\)

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
1472.2.a \(\chi_{1472}(1, \cdot)\) 1472.2.a.a 1 1
1472.2.a.b 1
1472.2.a.c 1
1472.2.a.d 1
1472.2.a.e 1
1472.2.a.f 1
1472.2.a.g 1
1472.2.a.h 1
1472.2.a.i 1
1472.2.a.j 1
1472.2.a.k 1
1472.2.a.l 1
1472.2.a.m 1
1472.2.a.n 1
1472.2.a.o 2
1472.2.a.p 2
1472.2.a.q 2
1472.2.a.r 2
1472.2.a.s 2
1472.2.a.t 2
1472.2.a.u 2
1472.2.a.v 2
1472.2.a.w 3
1472.2.a.x 3
1472.2.a.y 4
1472.2.a.z 4
1472.2.b \(\chi_{1472}(737, \cdot)\) 1472.2.b.a 6 1
1472.2.b.b 6
1472.2.b.c 16
1472.2.b.d 16
1472.2.c \(\chi_{1472}(1471, \cdot)\) 1472.2.c.a 4 1
1472.2.c.b 4
1472.2.c.c 6
1472.2.c.d 8
1472.2.c.e 24
1472.2.h \(\chi_{1472}(735, \cdot)\) 1472.2.h.a 8 1
1472.2.h.b 8
1472.2.h.c 32
1472.2.i \(\chi_{1472}(367, \cdot)\) 1472.2.i.a 12 2
1472.2.i.b 80
1472.2.j \(\chi_{1472}(369, \cdot)\) 1472.2.j.a 2 2
1472.2.j.b 4
1472.2.j.c 12
1472.2.j.d 24
1472.2.j.e 46
1472.2.m \(\chi_{1472}(185, \cdot)\) None 0 4
1472.2.n \(\chi_{1472}(183, \cdot)\) None 0 4
1472.2.q \(\chi_{1472}(193, \cdot)\) n/a 460 10
1472.2.r \(\chi_{1472}(93, \cdot)\) n/a 1408 8
1472.2.u \(\chi_{1472}(91, \cdot)\) n/a 1520 8
1472.2.v \(\chi_{1472}(159, \cdot)\) n/a 480 10
1472.2.ba \(\chi_{1472}(63, \cdot)\) n/a 460 10
1472.2.bb \(\chi_{1472}(225, \cdot)\) n/a 480 10
1472.2.be \(\chi_{1472}(49, \cdot)\) n/a 920 20
1472.2.bf \(\chi_{1472}(15, \cdot)\) n/a 920 20
1472.2.bi \(\chi_{1472}(7, \cdot)\) None 0 40
1472.2.bj \(\chi_{1472}(9, \cdot)\) None 0 40
1472.2.bk \(\chi_{1472}(11, \cdot)\) n/a 15200 80
1472.2.bn \(\chi_{1472}(13, \cdot)\) n/a 15200 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1472))\) into lower level spaces

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