↑

Properties

Label 1.12.a
Level $1$
Weight $12$
Character orbit 1.a
Rep. character $\chi_{1}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $1$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(1\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(1))\).

Total New Old
Modular forms 2 2 0
Cusp forms 1 1 0
Eisenstein series 1 1 0

Trace form

\( q - 24 q^{2} + 252 q^{3} - 1472 q^{4} + 4830 q^{5} - 6048 q^{6} - 16744 q^{7} + 84480 q^{8} - 113643 q^{9} + O(q^{10}) \) \( q - 24 q^{2} + 252 q^{3} - 1472 q^{4} + 4830 q^{5} - 6048 q^{6} - 16744 q^{7} + 84480 q^{8} - 113643 q^{9} - 115920 q^{10} + 534612 q^{11} - 370944 q^{12} - 577738 q^{13} + 401856 q^{14} + 1217160 q^{15} + 987136 q^{16} - 6905934 q^{17} + 2727432 q^{18} + 10661420 q^{19} - 7109760 q^{20} - 4219488 q^{21} - 12830688 q^{22} + 18643272 q^{23} + 21288960 q^{24} - 25499225 q^{25} + 13865712 q^{26} - 73279080 q^{27} + 24647168 q^{28} + 128406630 q^{29} - 29211840 q^{30} - 52843168 q^{31} - 196706304 q^{32} + 134722224 q^{33} + 165742416 q^{34} - 80873520 q^{35} + 167282496 q^{36} - 182213314 q^{37} - 255874080 q^{38} - 145589976 q^{39} + 408038400 q^{40} + 308120442 q^{41} + 101267712 q^{42} - 17125708 q^{43} - 786948864 q^{44} - 548895690 q^{45} - 447438528 q^{46} + 2687348496 q^{47} + 248758272 q^{48} - 1696965207 q^{49} + 611981400 q^{50} - 1740295368 q^{51} + 850430336 q^{52} - 1596055698 q^{53} + 1758697920 q^{54} + 2582175960 q^{55} - 1414533120 q^{56} + 2686677840 q^{57} - 3081759120 q^{58} - 5189203740 q^{59} - 1791659520 q^{60} + 6956478662 q^{61} + 1268236032 q^{62} + 1902838392 q^{63} + 2699296768 q^{64} - 2790474540 q^{65} - 3233333376 q^{66} - 15481826884 q^{67} + 10165534848 q^{68} + 4698104544 q^{69} + 1940964480 q^{70} + 9791485272 q^{71} - 9600560640 q^{72} + 1463791322 q^{73} + 4373119536 q^{74} - 6425804700 q^{75} - 15693610240 q^{76} - 8951543328 q^{77} + 3494159424 q^{78} + 38116845680 q^{79} + 4767866880 q^{80} + 1665188361 q^{81} - 7394890608 q^{82} - 29335099668 q^{83} + 6211086336 q^{84} - 33355661220 q^{85} + 411016992 q^{86} + 32358470760 q^{87} + 45164021760 q^{88} - 24992917110 q^{89} + 13173496560 q^{90} + 9673645072 q^{91} - 27442896384 q^{92} - 13316478336 q^{93} - 64496363904 q^{94} + 51494658600 q^{95} - 49569988608 q^{96} + 75013568546 q^{97} + 40727164968 q^{98} - 60754911516 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1.12.a.a 1.a 1.a $1$ $0.768$ \(\Q\) None 1.12.a.a \(-24\) \(252\) \(4830\) \(-16744\) $+$ $\mathrm{SU}(2)$ \(q-24q^{2}+252q^{3}-1472q^{4}+4830q^{5}+\cdots\)