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Properties

Label 23.16
Level 23
Weight 16
Dimension 317
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 704
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 16 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(704\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(23))\).

Total New Old
Modular forms 341 337 4
Cusp forms 319 317 2
Eisenstein series 22 20 2

Trace form

\( 317 q - 443 q^{2} + 6685 q^{3} - 27787 q^{4} - 104231 q^{5} + 1446325 q^{6} - 5644923 q^{7} + 8156149 q^{8} + 6279595 q^{9} + O(q^{10}) \) \( 317 q - 443 q^{2} + 6685 q^{3} - 27787 q^{4} - 104231 q^{5} + 1446325 q^{6} - 5644923 q^{7} + 8156149 q^{8} + 6279595 q^{9} - 22511531 q^{10} - 41173715 q^{11} + 92994037 q^{12} + 380146665 q^{13} - 1219301003 q^{14} - 1172234545 q^{15} + 11493859317 q^{16} - 8631001255 q^{17} + 15751387013 q^{18} + 2411205179 q^{19} - 57559068427 q^{20} + 14770604665 q^{21} + 45982353450 q^{22} - 9142981839 q^{23} - 336003502102 q^{24} + 35683424871 q^{25} + 268820155605 q^{26} + 8595164503 q^{27} - 746928094219 q^{28} - 19525596451 q^{29} + 1427169583733 q^{30} - 132785214865 q^{31} - 1064978907147 q^{32} + 1679518633133 q^{33} + 2538059229067 q^{34} - 2471979333081 q^{35} + 6525685313242 q^{36} + 796685652309 q^{37} - 7808676165216 q^{38} + 1007511192601 q^{39} + 15846103122589 q^{40} - 3047003248665 q^{41} - 20295513254765 q^{42} - 7045987039311 q^{43} + 9908440869844 q^{44} + 24989414174888 q^{45} + 15168220384237 q^{46} - 6362512814562 q^{47} - 61402824651555 q^{48} - 23159006226107 q^{49} + 53837911020914 q^{50} + 53489049797545 q^{51} + 37569662163807 q^{52} - 37264820749833 q^{53} - 62233637831571 q^{54} - 58909088551379 q^{55} + 195508975805934 q^{56} + 149507756959393 q^{57} - 233641939373708 q^{58} - 165571891747001 q^{59} + 52348733435879 q^{60} + 109740049971225 q^{61} + 198611418727669 q^{62} + 39147360093135 q^{63} - 339168102711307 q^{64} - 343082372555899 q^{65} - 104032766332836 q^{66} + 138939479040105 q^{67} + 841700562693866 q^{68} + 285577690343745 q^{69} - 227349803788054 q^{70} - 706278984481065 q^{71} - 1265410586420900 q^{72} + 99450391437729 q^{73} + 480827865274912 q^{74} + 1516772808675507 q^{75} - 662162328423806 q^{76} - 14989100576219 q^{77} + 1246125393266123 q^{78} - 709827170411791 q^{79} - 2053011537574870 q^{80} - 1413966792543481 q^{81} + 727228399224775 q^{82} + 1137673815673475 q^{83} + 874898436269667 q^{84} + 1352592293554731 q^{85} - 536947900449125 q^{86} - 5320017768380543 q^{87} - 2540260469311587 q^{88} - 1496386672137581 q^{89} + 7109739257448022 q^{90} + 5620444236900562 q^{91} + 3791345301430774 q^{92} + 579713258353022 q^{93} - 2999829490271316 q^{94} - 5616165586031105 q^{95} - 11597815512020580 q^{96} - 6872325161347245 q^{97} + 4069308624954589 q^{98} + 21102480405268471 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(23))\)

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
23.16.a \(\chi_{23}(1, \cdot)\) 23.16.a.a 12 1
23.16.a.b 15
23.16.c \(\chi_{23}(2, \cdot)\) 23.16.c.a 290 10

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(23))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(23)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)