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Properties

Label 12.21.d
Level $12$
Weight $21$
Character orbit 12.d
Rep. character $\chi_{12}(7,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $1$
Sturm bound $42$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 21 \)
Character orbit: \([\chi]\) \(=\) 12.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(42\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{21}(12, [\chi])\).

Total New Old
Modular forms 42 20 22
Cusp forms 38 20 18
Eisenstein series 4 0 4

Trace form

\( 20 q + 1254 q^{2} - 485524 q^{4} + 1476984 q^{5} - 36019890 q^{6} + 434160000 q^{8} - 23245229340 q^{9} + O(q^{10}) \) \( 20 q + 1254 q^{2} - 485524 q^{4} + 1476984 q^{5} - 36019890 q^{6} + 434160000 q^{8} - 23245229340 q^{9} + 3166779028 q^{10} + 35789598900 q^{12} - 197410187576 q^{13} + 1179712421976 q^{14} + 1592658749552 q^{16} + 4951946877000 q^{17} - 1457475879618 q^{18} - 20688414141528 q^{20} - 19078957703376 q^{21} + 54807260127768 q^{22} + 58196896476048 q^{24} + 513048947332092 q^{25} - 142319404376100 q^{26} - 1064314324942128 q^{28} - 1120225678237608 q^{29} + 919562090032260 q^{30} + 926940361437984 q^{32} - 1250504741372400 q^{33} + 1615904447739868 q^{34} + 564305836503708 q^{36} + 13452822768639208 q^{37} + 30625874417040840 q^{38} - 42278345025251456 q^{40} + 26778887480335560 q^{41} + 34752013424992728 q^{42} - 160483087306778736 q^{44} - 1716641590575528 q^{45} + 312713467885194624 q^{46} - 170793646915261968 q^{48} - 198082137742572844 q^{49} + 575620844246091282 q^{50} - 896547684604982408 q^{52} + 241769380233802968 q^{53} + 41864530192578630 q^{54} - 2099928347597457216 q^{56} + 595468774322860464 q^{57} + 1656374273217670084 q^{58} + 94322711748139416 q^{60} + 430703667006221224 q^{61} + 1718273064332222664 q^{62} - 3197273374119743872 q^{64} - 1146808855391494992 q^{65} + 1921733716920631128 q^{66} + 4484111570418829944 q^{68} - 4519043719923504960 q^{69} - 12213680959006457904 q^{70} - 504607438512720000 q^{72} + 12562724768160620200 q^{73} - 22136012572796109780 q^{74} + 28495592855672115888 q^{76} + 19985445258493440192 q^{77} - 20625251537531633940 q^{78} + 49505459663687019552 q^{80} + 27017034353459841780 q^{81} - 50718250504081238180 q^{82} + 24536705912722373616 q^{84} - 15354475681609135696 q^{85} - 85391409389241086952 q^{86} + 66078172926918803520 q^{88} + 43679060294354361384 q^{89} - 3680625238748114076 q^{90} - 64869958570030809216 q^{92} - 50732545022865845424 q^{93} + 95503492747592513424 q^{94} - 89530085825201077920 q^{96} + 7230988441427384872 q^{97} + 304648861287114073350 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{21}^{\mathrm{new}}(12, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
12.21.d.a 12.d 4.b $20$ $30.422$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(1254\) \(0\) \(1476984\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(63-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{3}+\cdots\)

Decomposition of \(S_{21}^{\mathrm{old}}(12, [\chi])\) into lower level spaces

\( S_{21}^{\mathrm{old}}(12, [\chi]) \cong \) \(S_{21}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 2}\)