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Properties

Label 1672.2
Level 1672
Weight 2
Dimension 46912
Nonzero newspaces 36
Sturm bound 345600
Trace bound 17

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Defining parameters

Level: \( N \) = \( 1672 = 2^{3} \cdot 11 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(345600\)
Trace bound: \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1672))\).

Total New Old
Modular forms 88560 48136 40424
Cusp forms 84241 46912 37329
Eisenstein series 4319 1224 3095

Trace form

\( 46912 q - 124 q^{2} - 124 q^{3} - 124 q^{4} - 124 q^{6} - 124 q^{7} - 124 q^{8} - 248 q^{9} + O(q^{10}) \) \( 46912 q - 124 q^{2} - 124 q^{3} - 124 q^{4} - 124 q^{6} - 124 q^{7} - 124 q^{8} - 248 q^{9} - 124 q^{10} - 142 q^{11} - 284 q^{12} - 124 q^{14} - 104 q^{15} - 124 q^{16} - 228 q^{17} - 124 q^{18} - 119 q^{19} - 268 q^{20} + 40 q^{21} - 142 q^{22} - 264 q^{23} - 124 q^{24} - 208 q^{25} - 124 q^{26} - 76 q^{27} - 124 q^{28} + 56 q^{29} - 184 q^{30} - 68 q^{31} - 144 q^{32} - 260 q^{33} - 364 q^{34} - 112 q^{35} - 284 q^{36} + 36 q^{37} - 184 q^{38} - 280 q^{39} - 264 q^{40} - 272 q^{41} - 344 q^{42} - 132 q^{43} - 282 q^{44} + 48 q^{45} - 264 q^{46} - 148 q^{47} - 344 q^{48} - 272 q^{49} - 264 q^{50} - 216 q^{51} - 224 q^{52} + 40 q^{53} - 392 q^{54} - 162 q^{55} - 364 q^{56} - 243 q^{57} - 288 q^{58} - 54 q^{59} - 296 q^{60} + 4 q^{61} - 304 q^{62} - 248 q^{63} - 412 q^{64} - 276 q^{65} - 286 q^{66} - 420 q^{67} - 376 q^{68} + 80 q^{69} - 416 q^{70} - 192 q^{71} - 564 q^{72} - 430 q^{73} - 312 q^{74} - 502 q^{75} - 414 q^{76} - 34 q^{77} - 404 q^{78} - 536 q^{79} - 192 q^{80} - 460 q^{81} - 464 q^{82} - 422 q^{83} - 316 q^{84} - 120 q^{85} - 256 q^{86} - 560 q^{87} + 34 q^{88} - 736 q^{89} - 132 q^{90} - 488 q^{91} - 144 q^{92} - 96 q^{93} + 44 q^{94} - 142 q^{95} - 128 q^{96} - 206 q^{97} + 96 q^{98} - 179 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1672))\)

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
1672.2.a \(\chi_{1672}(1, \cdot)\) 1672.2.a.a 1 1
1672.2.a.b 1
1672.2.a.c 1
1672.2.a.d 2
1672.2.a.e 3
1672.2.a.f 4
1672.2.a.g 5
1672.2.a.h 6
1672.2.a.i 6
1672.2.a.j 6
1672.2.a.k 9
1672.2.c \(\chi_{1672}(683, \cdot)\) n/a 200 1
1672.2.e \(\chi_{1672}(837, \cdot)\) n/a 180 1
1672.2.f \(\chi_{1672}(417, \cdot)\) 1672.2.f.a 2 1
1672.2.f.b 2
1672.2.f.c 28
1672.2.f.d 28
1672.2.h \(\chi_{1672}(1407, \cdot)\) None 0 1
1672.2.j \(\chi_{1672}(1253, \cdot)\) n/a 236 1
1672.2.l \(\chi_{1672}(571, \cdot)\) n/a 216 1
1672.2.o \(\chi_{1672}(1519, \cdot)\) None 0 1
1672.2.q \(\chi_{1672}(353, \cdot)\) 1672.2.q.a 2 2
1672.2.q.b 2
1672.2.q.c 2
1672.2.q.d 4
1672.2.q.e 4
1672.2.q.f 18
1672.2.q.g 18
1672.2.q.h 24
1672.2.q.i 26
1672.2.r \(\chi_{1672}(609, \cdot)\) n/a 216 4
1672.2.s \(\chi_{1672}(639, \cdot)\) None 0 2
1672.2.w \(\chi_{1672}(373, \cdot)\) n/a 472 2
1672.2.y \(\chi_{1672}(923, \cdot)\) n/a 472 2
1672.2.ba \(\chi_{1672}(65, \cdot)\) n/a 120 2
1672.2.bc \(\chi_{1672}(87, \cdot)\) None 0 2
1672.2.bd \(\chi_{1672}(331, \cdot)\) n/a 400 2
1672.2.bf \(\chi_{1672}(45, \cdot)\) n/a 400 2
1672.2.bh \(\chi_{1672}(177, \cdot)\) n/a 300 6
1672.2.bj \(\chi_{1672}(455, \cdot)\) None 0 4
1672.2.bm \(\chi_{1672}(723, \cdot)\) n/a 864 4
1672.2.bo \(\chi_{1672}(189, \cdot)\) n/a 944 4
1672.2.bq \(\chi_{1672}(39, \cdot)\) None 0 4
1672.2.bs \(\chi_{1672}(569, \cdot)\) n/a 240 4
1672.2.bt \(\chi_{1672}(229, \cdot)\) n/a 864 4
1672.2.bv \(\chi_{1672}(75, \cdot)\) n/a 944 4
1672.2.bx \(\chi_{1672}(49, \cdot)\) n/a 480 8
1672.2.bz \(\chi_{1672}(43, \cdot)\) n/a 1416 6
1672.2.cb \(\chi_{1672}(309, \cdot)\) n/a 1200 6
1672.2.ce \(\chi_{1672}(175, \cdot)\) None 0 6
1672.2.cf \(\chi_{1672}(287, \cdot)\) None 0 6
1672.2.ci \(\chi_{1672}(21, \cdot)\) n/a 1416 6
1672.2.ck \(\chi_{1672}(67, \cdot)\) n/a 1200 6
1672.2.cl \(\chi_{1672}(241, \cdot)\) n/a 360 6
1672.2.co \(\chi_{1672}(125, \cdot)\) n/a 1888 8
1672.2.cq \(\chi_{1672}(27, \cdot)\) n/a 1888 8
1672.2.cr \(\chi_{1672}(7, \cdot)\) None 0 8
1672.2.ct \(\chi_{1672}(145, \cdot)\) n/a 480 8
1672.2.cv \(\chi_{1672}(83, \cdot)\) n/a 1888 8
1672.2.cx \(\chi_{1672}(293, \cdot)\) n/a 1888 8
1672.2.db \(\chi_{1672}(31, \cdot)\) None 0 8
1672.2.dc \(\chi_{1672}(9, \cdot)\) n/a 1440 24
1672.2.de \(\chi_{1672}(41, \cdot)\) n/a 1440 24
1672.2.df \(\chi_{1672}(3, \cdot)\) n/a 5664 24
1672.2.dh \(\chi_{1672}(13, \cdot)\) n/a 5664 24
1672.2.dk \(\chi_{1672}(15, \cdot)\) None 0 24
1672.2.dl \(\chi_{1672}(63, \cdot)\) None 0 24
1672.2.do \(\chi_{1672}(5, \cdot)\) n/a 5664 24
1672.2.dq \(\chi_{1672}(35, \cdot)\) n/a 5664 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1672))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1672)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(209))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(418))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(836))\)\(^{\oplus 2}\)