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Properties

Label 12.9
Level 12
Weight 9
Dimension 11
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 72
Trace bound 1

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Defining parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(72\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(12))\).

Total New Old
Modular forms 37 11 26
Cusp forms 27 11 16
Eisenstein series 10 0 10

Trace form

\( 11 q + 6 q^{2} - 21 q^{3} - 52 q^{4} - 336 q^{5} + 1134 q^{6} - 2154 q^{7} - 12960 q^{8} - 13653 q^{9} + O(q^{10}) \) \( 11 q + 6 q^{2} - 21 q^{3} - 52 q^{4} - 336 q^{5} + 1134 q^{6} - 2154 q^{7} - 12960 q^{8} - 13653 q^{9} + 36628 q^{10} - 11340 q^{12} - 53258 q^{13} + 52728 q^{14} + 142560 q^{15} + 99440 q^{16} - 193200 q^{17} - 13122 q^{18} - 419178 q^{19} + 335592 q^{20} + 764166 q^{21} - 556968 q^{22} + 221616 q^{24} - 1973253 q^{25} + 21564 q^{26} + 1477899 q^{27} - 594672 q^{28} + 2063472 q^{29} + 46980 q^{30} - 937578 q^{31} - 3602784 q^{32} - 777600 q^{33} + 1568476 q^{34} + 113724 q^{36} + 10292470 q^{37} + 3659400 q^{38} - 2156298 q^{39} + 1749184 q^{40} - 8865456 q^{41} - 5288328 q^{42} + 5472726 q^{43} + 2395920 q^{44} - 13806288 q^{45} - 13649856 q^{46} + 10916208 q^{48} - 799471 q^{49} + 14581842 q^{50} - 7413120 q^{51} + 18592888 q^{52} + 8706672 q^{53} - 2480058 q^{54} - 2566080 q^{55} - 45565632 q^{56} - 15072378 q^{57} - 8816444 q^{58} + 28348056 q^{60} + 28369078 q^{61} + 80783976 q^{62} + 34876566 q^{63} + 1268864 q^{64} + 7293408 q^{65} - 51205608 q^{66} - 61469994 q^{67} - 117288264 q^{68} + 3623616 q^{69} - 60373104 q^{70} + 28343520 q^{72} + 60447958 q^{73} + 119548428 q^{74} + 122666955 q^{75} + 144621360 q^{76} - 56971392 q^{77} - 140630580 q^{78} - 145689834 q^{79} - 163857888 q^{80} + 2604555 q^{81} - 188383460 q^{82} + 199712304 q^{84} - 67764256 q^{85} + 240327384 q^{86} + 108773280 q^{87} + 156323520 q^{88} + 188992272 q^{89} - 80105436 q^{90} - 99306132 q^{91} - 387657984 q^{92} - 245827770 q^{93} - 38749872 q^{94} + 246092256 q^{96} + 92717014 q^{97} + 691081830 q^{98} - 14541120 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(12))\)

We only show spaces with odd 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
12.9.c \(\chi_{12}(5, \cdot)\) 12.9.c.a 1 1
12.9.c.b 2
12.9.d \(\chi_{12}(7, \cdot)\) 12.9.d.a 8 1

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(12))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(12)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)