Properties

Label 14.12.c
Level $14$
Weight $12$
Character orbit 14.c
Rep. character $\chi_{14}(9,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
Newform subspaces $2$
Sturm bound $24$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 14.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(14, [\chi])\).

Total New Old
Modular forms 48 16 32
Cusp forms 40 16 24
Eisenstein series 8 0 8

Trace form

\( 16 q - 8192 q^{4} + 11312 q^{5} - 34048 q^{6} + 68104 q^{7} - 627368 q^{9} + O(q^{10}) \) \( 16 q - 8192 q^{4} + 11312 q^{5} - 34048 q^{6} + 68104 q^{7} - 627368 q^{9} + 118272 q^{10} + 1133176 q^{11} - 1612240 q^{13} + 2654336 q^{14} + 1775056 q^{15} - 8388608 q^{16} + 10187968 q^{17} + 12170496 q^{18} - 14318920 q^{19} - 23166976 q^{20} - 41167352 q^{21} + 45255936 q^{22} + 61861024 q^{23} + 17432576 q^{24} - 196562000 q^{25} + 57714944 q^{26} + 175695408 q^{27} - 65282048 q^{28} - 7839472 q^{29} - 44415104 q^{30} + 291871496 q^{31} + 325323992 q^{33} - 481313280 q^{34} - 1737885464 q^{35} + 1284849664 q^{36} + 634648088 q^{37} + 921105024 q^{38} - 159200840 q^{39} + 121110528 q^{40} - 4929818544 q^{41} - 2762479872 q^{42} + 3777176000 q^{43} + 1160372224 q^{44} + 9655050104 q^{45} - 2661097344 q^{46} + 1329789720 q^{47} - 15841003184 q^{49} + 2704160768 q^{50} + 13918649240 q^{51} + 825466880 q^{52} - 8634346872 q^{53} + 2202736256 q^{54} - 24498433344 q^{55} - 4998823936 q^{56} + 22974199632 q^{57} + 6959834880 q^{58} + 21384302240 q^{59} - 908828672 q^{60} + 4377938936 q^{61} - 43557826816 q^{62} - 29085810312 q^{63} + 17179869184 q^{64} + 36121112328 q^{65} + 20941383680 q^{66} + 968573360 q^{67} + 10432479232 q^{68} - 61447316896 q^{69} - 13888060032 q^{70} + 24699254176 q^{71} + 12462587904 q^{72} + 25151800184 q^{73} + 9331647744 q^{74} - 27465986576 q^{75} + 29325148160 q^{76} - 687714496 q^{77} - 73411176448 q^{78} - 48025080160 q^{79} + 11861491712 q^{80} + 3502213696 q^{81} - 27109947648 q^{82} + 176845941664 q^{83} + 56780701696 q^{84} - 38209307952 q^{85} - 33225867264 q^{86} - 295758917048 q^{87} - 23171039232 q^{88} + 55149699528 q^{89} + 250430620160 q^{90} + 233972705648 q^{91} - 126691377152 q^{92} - 204137018504 q^{93} - 99775111296 q^{94} + 153407449936 q^{95} + 17850957824 q^{96} + 150068913008 q^{97} + 347442899712 q^{98} - 152071856816 q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(14, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
14.12.c.a 14.c 7.c $8$ $10.757$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-128\) \(266\) \(7504\) \(-42224\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2^{5}+2^{5}\beta _{2})q^{2}+(67\beta _{2}-\beta _{3})q^{3}+\cdots\)
14.12.c.b 14.c 7.c $8$ $10.757$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(128\) \(-266\) \(3808\) \(110328\) $\mathrm{SU}(2)[C_{3}]$ \(q+2^{5}\beta _{2}q^{2}+(-67+\beta _{1}+67\beta _{2})q^{3}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(14, [\chi]) \cong \) \(S_{12}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)