Properties

Label 12.21
Level 12
Weight 21
Dimension 27
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 168
Trace bound 1

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Defining parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 21 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(168\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{21}(\Gamma_1(12))\).

Total New Old
Modular forms 85 27 58
Cusp forms 75 27 48
Eisenstein series 10 0 10

Trace form

\( 27 q + 1254 q^{2} - 25329 q^{3} - 485524 q^{4} + 1476984 q^{5} - 36019890 q^{6} - 222376306 q^{7} + 434160000 q^{8} - 27506419173 q^{9} + O(q^{10}) \) \( 27 q + 1254 q^{2} - 25329 q^{3} - 485524 q^{4} + 1476984 q^{5} - 36019890 q^{6} - 222376306 q^{7} + 434160000 q^{8} - 27506419173 q^{9} + 3166779028 q^{10} + 35789598900 q^{12} - 346980054522 q^{13} + 1179712421976 q^{14} - 534244714560 q^{15} + 1592658749552 q^{16} + 4951946877000 q^{17} - 1457475879618 q^{18} + 8358992819678 q^{19} - 20688414141528 q^{20} - 13083938040498 q^{21} + 54807260127768 q^{22} + 58196896476048 q^{24} + 371933683950547 q^{25} - 142319404376100 q^{26} - 63450256871169 q^{27} - 1064314324942128 q^{28} - 1120225678237608 q^{29} + 919562090032260 q^{30} + 146332698951278 q^{31} + 926940361437984 q^{32} - 1484171512069680 q^{33} + 1615904447739868 q^{34} + 564305836503708 q^{36} + 10500835324209990 q^{37} + 30625874417040840 q^{38} - 6116710685036082 q^{39} - 42278345025251456 q^{40} + 26778887480335560 q^{41} + 34752013424992728 q^{42} - 37931849279065666 q^{43} - 160483087306778736 q^{44} + 15269817785746392 q^{45} + 312713467885194624 q^{46} - 170793646915261968 q^{48} - 71985399577496119 q^{49} + 575620844246091282 q^{50} - 21650764841061120 q^{51} - 896547684604982408 q^{52} + 241769380233802968 q^{53} + 41864530192578630 q^{54} - 342407748800488320 q^{55} - 2099928347597457216 q^{56} + 764070320446363038 q^{57} + 1656374273217670084 q^{58} + 94322711748139416 q^{60} + 872138254323760422 q^{61} + 1718273064332222664 q^{62} + 1647033428075634414 q^{63} - 3197273374119743872 q^{64} - 1146808855391494992 q^{65} + 1921733716920631128 q^{66} - 1224537804813749986 q^{67} + 4484111570418829944 q^{68} - 3115653043739947200 q^{69} - 12213680959006457904 q^{70} - 504607438512720000 q^{72} + 1104392874037773462 q^{73} - 22136012572796109780 q^{74} + 8469463553745356895 q^{75} + 28495592855672115888 q^{76} + 19985445258493440192 q^{77} - 20625251537531633940 q^{78} - 21445740411143332306 q^{79} + 49505459663687019552 q^{80} + 59422926251535480027 q^{81} - 50718250504081238180 q^{82} + 24536705912722373616 q^{84} - 85877860616600907856 q^{85} - 85391409389241086952 q^{86} + 101352340532658519360 q^{87} + 66078172926918803520 q^{88} + 43679060294354361384 q^{89} - 3680625238748114076 q^{90} - 160172974474912127108 q^{91} - 64869958570030809216 q^{92} + 128599648539169062990 q^{93} + 95503492747592513424 q^{94} - 89530085825201077920 q^{96} - 331755395243910474954 q^{97} + 304648861287114073350 q^{98} + 475048517452037815680 q^{99} + O(q^{100}) \)

Decomposition of \(S_{21}^{\mathrm{new}}(\Gamma_1(12))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
12.21.c \(\chi_{12}(5, \cdot)\) 12.21.c.a 1 1
12.21.c.b 6
12.21.d \(\chi_{12}(7, \cdot)\) 12.21.d.a 20 1

Decomposition of \(S_{21}^{\mathrm{old}}(\Gamma_1(12))\) into lower level spaces

\( S_{21}^{\mathrm{old}}(\Gamma_1(12)) \cong \) \(S_{21}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)