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Properties

Label 12.18
Level 12
Weight 18
Dimension 34
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 144
Trace bound 1

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Defining parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 18 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(144\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(12))\).

Total New Old
Modular forms 73 38 35
Cusp forms 63 34 29
Eisenstein series 10 4 6

Trace form

\( 34 q - 54808 q^{4} - 1477980 q^{5} - 4960776 q^{6} - 24263960 q^{7} + 165968418 q^{9} + O(q^{10}) \) \( 34 q - 54808 q^{4} - 1477980 q^{5} - 4960776 q^{6} - 24263960 q^{7} + 165968418 q^{9} + 46839088 q^{10} - 1032380208 q^{11} + 2598308520 q^{12} - 652740340 q^{13} + 11415352680 q^{15} - 41721285088 q^{16} + 43735163220 q^{17} + 27568791600 q^{18} - 153568558640 q^{19} + 92741616744 q^{21} - 493958165040 q^{22} - 80527437360 q^{23} - 253565784288 q^{24} - 1983764722498 q^{25} - 2695436033040 q^{28} - 2282551050492 q^{29} - 2169979068432 q^{30} + 2168009129608 q^{31} - 21965600274360 q^{33} + 6944208632512 q^{34} + 13207404535920 q^{35} - 12909384040056 q^{36} - 46787236254100 q^{37} + 28716563238480 q^{39} + 21066454663744 q^{40} + 17740604240100 q^{41} + 55835180334480 q^{42} + 97730802970480 q^{43} + 90391071100836 q^{45} + 235918828815264 q^{46} - 172678557920400 q^{47} + 299462725247520 q^{48} - 404742697237870 q^{49} - 287565080446512 q^{51} + 544732086739120 q^{52} + 1087043089943700 q^{53} + 487051858173384 q^{54} + 190011694259520 q^{55} - 1891784499679080 q^{57} + 230877304263760 q^{58} - 182503267515072 q^{59} - 345098683994304 q^{60} - 7893665904338692 q^{61} - 1044483916475160 q^{63} + 1003775054518400 q^{64} + 4453501300162200 q^{65} - 2371521654206832 q^{66} - 669199133977280 q^{67} - 3453734292265632 q^{69} - 949041839387232 q^{70} + 12010628577638160 q^{71} + 5817303713532480 q^{72} - 6197649738579820 q^{73} - 16871662953986400 q^{75} - 2051936325547056 q^{76} + 14312669809183200 q^{77} + 22261766802491280 q^{78} - 12372197413768664 q^{79} + 31727349360455202 q^{81} + 7596239161270240 q^{82} + 43379661699213840 q^{83} - 8356700998055568 q^{84} - 10538064781908184 q^{85} - 33328475346849480 q^{87} - 18469777603302720 q^{88} + 98415339645711060 q^{89} - 68814047068261392 q^{90} - 1278589146387280 q^{91} - 80169926343741960 q^{93} - 61915224567506112 q^{94} + 147953880687427200 q^{95} - 45410293501908864 q^{96} - 879948917195740 q^{97} - 44440582779697968 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(12))\)

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
12.18.a \(\chi_{12}(1, \cdot)\) 12.18.a.a 1 1
12.18.a.b 1
12.18.b \(\chi_{12}(11, \cdot)\) 12.18.b.a 32 1

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(12))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(12)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)