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Properties

Label 12.13.d
Level $12$
Weight $13$
Character orbit 12.d
Rep. character $\chi_{12}(7,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $1$
Sturm bound $26$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 13 \)
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: \(26\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(12, [\chi])\).

Total New Old
Modular forms 26 12 14
Cusp forms 22 12 10
Eisenstein series 4 0 4

Trace form

\( 12 q - 90 q^{2} - 4692 q^{4} - 10296 q^{5} - 48114 q^{6} - 648000 q^{8} - 2125764 q^{9} + O(q^{10}) \) \( 12 q - 90 q^{2} - 4692 q^{4} - 10296 q^{5} - 48114 q^{6} - 648000 q^{8} - 2125764 q^{9} + 923028 q^{10} - 3018060 q^{12} + 2094840 q^{13} + 15389208 q^{14} - 61526928 q^{16} - 12097800 q^{17} + 15943230 q^{18} - 377644248 q^{20} - 75057840 q^{21} + 482545560 q^{22} - 332039088 q^{24} + 1058748132 q^{25} + 243358236 q^{26} - 185369520 q^{28} + 1997608680 q^{29} - 577761660 q^{30} + 1733536800 q^{32} + 322101360 q^{33} - 7816269348 q^{34} + 831173724 q^{36} - 960170280 q^{37} - 8280525240 q^{38} + 3985807104 q^{40} + 5806392696 q^{41} - 1390844520 q^{42} + 4989496464 q^{44} + 1823905512 q^{45} + 4149450240 q^{46} - 7791843600 q^{48} - 60479071668 q^{49} + 68552901522 q^{50} - 31090133640 q^{52} + 42482511720 q^{53} + 8523250758 q^{54} - 38053468224 q^{56} - 58319941680 q^{57} + 159666562500 q^{58} - 19968517224 q^{60} + 137368568088 q^{61} - 27876030840 q^{62} + 188355529344 q^{64} - 328250713392 q^{65} - 136719325224 q^{66} + 77938316280 q^{68} + 214339017024 q^{69} - 454939318704 q^{70} + 114791256000 q^{72} - 804477880680 q^{73} - 502785766548 q^{74} + 143972453808 q^{76} + 1383727360320 q^{77} - 72052158420 q^{78} - 417712547808 q^{80} + 376572715308 q^{81} + 460673773020 q^{82} + 28008331632 q^{84} + 1437981718224 q^{85} + 1255416205464 q^{86} + 47622991680 q^{88} - 1422946205928 q^{89} - 163511641116 q^{90} - 3462722444160 q^{92} + 1056734080560 q^{93} + 847910842896 q^{94} + 341032101984 q^{96} - 4056673857000 q^{97} + 1702751294790 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{13}^{\mathrm{new}}(12, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
12.13.d.a 12.d 4.b $12$ $10.968$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-90\) \(0\) \(-10296\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-8+\beta _{2})q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-386+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{13}^{\mathrm{old}}(12, [\chi])\) into lower level spaces

\( S_{13}^{\mathrm{old}}(12, [\chi]) \cong \) \(S_{13}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 2}\)