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Properties

Label 23.18
Level 23
Weight 18
Dimension 361
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 792
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 18 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(792\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(23))\).

Total New Old
Modular forms 385 381 4
Cusp forms 363 361 2
Eisenstein series 22 20 2

Trace form

\( 361 q + 1045 q^{2} + 8557 q^{3} - 295435 q^{4} + 2051689 q^{5} - 4523915 q^{6} - 6451995 q^{7} + 17571829 q^{8} + 221575003 q^{9} + O(q^{10}) \) \( 361 q + 1045 q^{2} + 8557 q^{3} - 295435 q^{4} + 2051689 q^{5} - 4523915 q^{6} - 6451995 q^{7} + 17571829 q^{8} + 221575003 q^{9} - 1083297611 q^{10} + 1507236445 q^{11} + 1265596405 q^{12} - 5082129063 q^{13} + 3406647541 q^{14} - 71036660122 q^{15} + 68907171829 q^{16} + 3239146724 q^{17} + 142255198613 q^{18} - 192401658350 q^{19} + 1192787670005 q^{20} + 383995356778 q^{21} - 2003090066582 q^{22} + 669393119151 q^{23} + 6888149385194 q^{24} - 2164368311123 q^{25} - 1524711994443 q^{26} + 4620756886156 q^{27} + 12773801914357 q^{28} - 11081078455480 q^{29} - 4511648708875 q^{30} + 32960256696166 q^{31} - 65076944306187 q^{32} + 45250433938424 q^{33} + 53874839004107 q^{34} + 21590446692639 q^{35} + 97532037494962 q^{36} - 216882372343939 q^{37} + 195500729581344 q^{38} + 187366428705049 q^{39} - 527101981439011 q^{40} - 215135092413813 q^{41} + 724961045316211 q^{42} + 628640877405233 q^{43} - 85647082376900 q^{44} - 1337101003893172 q^{45} - 717848002140115 q^{46} + 939748893776670 q^{47} + 2014508628145437 q^{48} - 40257840879167 q^{49} - 2878414733211886 q^{50} - 1078795891675271 q^{51} + 3889005014349455 q^{52} + 1420076451264435 q^{53} + 3893271406559469 q^{54} - 9495580347527813 q^{55} + 9881481590177142 q^{56} + 6659398544225482 q^{57} - 5771319790493180 q^{58} - 3586310114020133 q^{59} + 33362144250195479 q^{60} + 3045105651805877 q^{61} - 23922633782091275 q^{62} - 8926923192883278 q^{63} + 15922450902548469 q^{64} + 30165354853397522 q^{65} + 19468621317861012 q^{66} - 14930105655103577 q^{67} - 58741471439692822 q^{68} - 16080877240870872 q^{69} + 19462045395308010 q^{70} + 43334897514643770 q^{71} + 58767815657250964 q^{72} - 12917433146581865 q^{73} - 100641814443817064 q^{74} - 101441635206266892 q^{75} - 12253348964186022 q^{76} + 171308830482454852 q^{77} + 47499379461584699 q^{78} - 124069024934626035 q^{79} - 333313970033793310 q^{80} + 176985853746937547 q^{81} + 290961180772556151 q^{82} + 142950913802513960 q^{83} - 610585250520034317 q^{84} - 334868726037525603 q^{85} + 157972863742569931 q^{86} + 403077304159698817 q^{87} + 280589247167559517 q^{88} + 2400718345498975 q^{89} - 442551565315234562 q^{90} - 430217131966053454 q^{91} - 274740046780894802 q^{92} + 68219474217143462 q^{93} + 483733470123421188 q^{94} + 767099884850904550 q^{95} + 106233145212999684 q^{96} - 366154725832534224 q^{97} - 417908215739157011 q^{98} - 855776355235963766 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(23))\)

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
23.18.a \(\chi_{23}(1, \cdot)\) 23.18.a.a 14 1
23.18.a.b 17
23.18.c \(\chi_{23}(2, \cdot)\) 23.18.c.a 330 10

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(23))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(23)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)