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Properties

Label 12.19.d
Level $12$
Weight $19$
Character orbit 12.d
Rep. character $\chi_{12}(7,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $1$
Sturm bound $38$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 19 \)
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: \(38\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{19}(12, [\chi])\).

Total New Old
Modular forms 38 18 20
Cusp forms 34 18 16
Eisenstein series 4 0 4

Trace form

\( 18 q - 170 q^{2} - 436932 q^{4} - 1721764 q^{5} - 6731586 q^{6} + 108558736 q^{8} - 2324522934 q^{9} + O(q^{10}) \) \( 18 q - 170 q^{2} - 436932 q^{4} - 1721764 q^{5} - 6731586 q^{6} + 108558736 q^{8} - 2324522934 q^{9} + 1397074644 q^{10} - 6468699852 q^{12} + 1799208612 q^{13} - 48147537912 q^{14} - 119537094672 q^{16} - 282984271180 q^{17} + 21953827710 q^{18} + 491637621128 q^{20} + 254050055640 q^{21} + 272503644408 q^{22} + 4483423343232 q^{24} + 20224739695878 q^{25} - 2765456970196 q^{26} + 27756503338032 q^{28} + 1812741883820 q^{29} - 3579410315772 q^{30} + 216191588070880 q^{32} + 17014318866216 q^{33} - 275796423660708 q^{34} + 56425469699916 q^{36} + 197439381411156 q^{37} - 676030464010008 q^{38} + 1941137842438368 q^{40} - 204669372669676 q^{41} - 1059935698181880 q^{42} + 3599128179401424 q^{44} + 222348883607532 q^{45} - 3847169819651040 q^{46} + 1457367907812912 q^{48} - 3424095824368878 q^{49} - 10192520264009358 q^{50} + 4228291003193208 q^{52} - 14112687314785972 q^{53} + 869318113288518 q^{54} - 6591066595001856 q^{56} - 9662233004693640 q^{57} + 17584741731886020 q^{58} + 193536143011224 q^{60} + 4171094773122132 q^{61} + 77227021488187896 q^{62} - 53424456043095936 q^{64} + 35585253307254712 q^{65} + 40644920520184824 q^{66} - 91403316760947112 q^{68} + 26342656148137824 q^{69} + 264958129332427248 q^{70} - 14019292862113968 q^{72} - 83809473755653692 q^{73} + 55949505142092092 q^{74} - 129026923617832848 q^{76} - 354619239852167328 q^{77} - 34535086926497028 q^{78} + 43257628406200352 q^{80} + 300189270593998242 q^{81} - 458290372754774916 q^{82} + 324078384809786832 q^{84} + 166017223439872920 q^{85} - 975848731010420424 q^{86} + 1151342491040801280 q^{88} - 660650117825905468 q^{89} - 180418447249326972 q^{90} + 1359275349780859584 q^{92} - 447365281400937432 q^{93} - 2087066679318498384 q^{94} + 257905715132447136 q^{96} + 2412557706093917220 q^{97} - 3767017570512990122 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{19}^{\mathrm{new}}(12, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
12.19.d.a 12.d 4.b $18$ $24.646$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-170\) \(0\) \(-1721764\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-9-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-24281+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{19}^{\mathrm{old}}(12, [\chi])\) into lower level spaces

\( S_{19}^{\mathrm{old}}(12, [\chi]) \cong \) \(S_{19}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 2}\)