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Properties

Label 3509.2
Level 3509
Weight 2
Dimension 494853
Nonzero newspaces 24
Sturm bound 2032800
Trace bound 2

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Defining parameters

Level: \( N \) = \( 3509 = 11^{2} \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(2032800\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3509))\).

Total New Old
Modular forms 512680 502439 10241
Cusp forms 503721 494853 8868
Eisenstein series 8959 7586 1373

Trace form

\( 494853 q - 1178 q^{2} - 1176 q^{3} - 1170 q^{4} - 1172 q^{5} - 1180 q^{6} - 1188 q^{7} - 1194 q^{8} - 1198 q^{9} + O(q^{10}) \) \( 494853 q - 1178 q^{2} - 1176 q^{3} - 1170 q^{4} - 1172 q^{5} - 1180 q^{6} - 1188 q^{7} - 1194 q^{8} - 1198 q^{9} - 1208 q^{10} - 1310 q^{11} - 2248 q^{12} - 1176 q^{13} - 1196 q^{14} - 1216 q^{15} - 1242 q^{16} - 1208 q^{17} - 1226 q^{18} - 1204 q^{19} - 1261 q^{20} - 1248 q^{21} - 1360 q^{22} - 2250 q^{23} - 1368 q^{24} - 1270 q^{25} - 1315 q^{26} - 1266 q^{27} - 1362 q^{28} - 1277 q^{29} - 2658 q^{30} - 1228 q^{31} - 1314 q^{32} - 1380 q^{33} - 2311 q^{34} - 1296 q^{35} - 1446 q^{36} - 1242 q^{37} - 1312 q^{38} - 1320 q^{39} - 1365 q^{40} - 1280 q^{41} - 1372 q^{42} - 1276 q^{43} - 1440 q^{44} - 2383 q^{45} - 1370 q^{46} - 1256 q^{47} - 1508 q^{48} - 1346 q^{49} - 1416 q^{50} - 1356 q^{51} - 1440 q^{52} - 1359 q^{53} - 1570 q^{54} - 1420 q^{55} - 2550 q^{56} - 1394 q^{57} - 1477 q^{58} - 2566 q^{59} - 1704 q^{60} - 1296 q^{61} - 1510 q^{62} - 1468 q^{63} - 1576 q^{64} - 1379 q^{65} - 1550 q^{66} - 2404 q^{67} - 1530 q^{68} - 1408 q^{69} - 1576 q^{70} - 1390 q^{71} - 1708 q^{72} - 1359 q^{73} - 1514 q^{74} - 1466 q^{75} - 1556 q^{76} - 1470 q^{77} - 2600 q^{78} - 1392 q^{79} - 1748 q^{80} - 1514 q^{81} - 1408 q^{82} - 1412 q^{83} - 1806 q^{84} - 1472 q^{85} - 1534 q^{86} - 1409 q^{87} - 3020 q^{88} - 2374 q^{89} - 1798 q^{90} - 1504 q^{91} - 1676 q^{92} - 1504 q^{93} - 1572 q^{94} - 1516 q^{95} - 1938 q^{96} - 1465 q^{97} - 1664 q^{98} - 1580 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3509))\)

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
3509.2.a \(\chi_{3509}(1, \cdot)\) 3509.2.a.a 1 1
3509.2.a.b 1
3509.2.a.c 1
3509.2.a.d 1
3509.2.a.e 1
3509.2.a.f 2
3509.2.a.g 2
3509.2.a.h 2
3509.2.a.i 2
3509.2.a.j 2
3509.2.a.k 3
3509.2.a.l 4
3509.2.a.m 7
3509.2.a.n 8
3509.2.a.o 9
3509.2.a.p 9
3509.2.a.q 11
3509.2.a.r 11
3509.2.a.s 11
3509.2.a.t 11
3509.2.a.u 22
3509.2.a.v 22
3509.2.a.w 24
3509.2.a.x 24
3509.2.a.y 32
3509.2.a.z 32
3509.2.b \(\chi_{3509}(2058, \cdot)\) n/a 264 1
3509.2.f \(\chi_{3509}(2419, \cdot)\) n/a 524 2
3509.2.g \(\chi_{3509}(1219, \cdot)\) n/a 1008 4
3509.2.h \(\chi_{3509}(364, \cdot)\) n/a 1578 6
3509.2.k \(\chi_{3509}(202, \cdot)\) n/a 1048 4
3509.2.l \(\chi_{3509}(320, \cdot)\) n/a 3080 10
3509.2.o \(\chi_{3509}(122, \cdot)\) n/a 1584 6
3509.2.p \(\chi_{3509}(215, \cdot)\) n/a 2096 8
3509.2.s \(\chi_{3509}(144, \cdot)\) n/a 3280 10
3509.2.u \(\chi_{3509}(362, \cdot)\) n/a 3144 12
3509.2.w \(\chi_{3509}(81, \cdot)\) n/a 6288 24
3509.2.x \(\chi_{3509}(186, \cdot)\) n/a 6560 20
3509.2.z \(\chi_{3509}(59, \cdot)\) n/a 12320 40
3509.2.ba \(\chi_{3509}(9, \cdot)\) n/a 6288 24
3509.2.bd \(\chi_{3509}(23, \cdot)\) n/a 19680 60
3509.2.bf \(\chi_{3509}(86, \cdot)\) n/a 13120 40
3509.2.bi \(\chi_{3509}(40, \cdot)\) n/a 12576 48
3509.2.bk \(\chi_{3509}(34, \cdot)\) n/a 19680 60
3509.2.bn \(\chi_{3509}(17, \cdot)\) n/a 26240 80
3509.2.bp \(\chi_{3509}(10, \cdot)\) n/a 39360 120
3509.2.bq \(\chi_{3509}(16, \cdot)\) n/a 78720 240
3509.2.bs \(\chi_{3509}(4, \cdot)\) n/a 78720 240
3509.2.bu \(\chi_{3509}(2, \cdot)\) n/a 157440 480

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3509))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3509)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(319))\)\(^{\oplus 2}\)