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Properties

Label 7.14.c
Level $7$
Weight $14$
Character orbit 7.c
Rep. character $\chi_{7}(2,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
Newform subspaces $1$
Sturm bound $9$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 7.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(7, [\chi])\).

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

Trace form

\( 16 q - 2 q^{2} + 728 q^{3} - 32588 q^{4} + 46928 q^{5} - 30212 q^{6} + 257992 q^{7} - 1093248 q^{8} - 2910808 q^{9} + O(q^{10}) \) \( 16 q - 2 q^{2} + 728 q^{3} - 32588 q^{4} + 46928 q^{5} - 30212 q^{6} + 257992 q^{7} - 1093248 q^{8} - 2910808 q^{9} + 879018 q^{10} + 3746000 q^{11} + 13786276 q^{12} - 63556528 q^{13} - 45497410 q^{14} + 179729504 q^{15} - 158020976 q^{16} + 108548496 q^{17} + 358872748 q^{18} + 617001728 q^{19} - 1844979416 q^{20} + 400815352 q^{21} + 977603772 q^{22} - 274288968 q^{23} - 690136272 q^{24} + 342571888 q^{25} - 1890370748 q^{26} + 1818768224 q^{27} - 2830532012 q^{28} - 1243557136 q^{29} + 8470546342 q^{30} + 1983953552 q^{31} - 18584336224 q^{32} - 3534705832 q^{33} + 35123983356 q^{34} - 15057013664 q^{35} + 2810399728 q^{36} + 3822948680 q^{37} + 48271561702 q^{38} + 5559167432 q^{39} + 20095902624 q^{40} - 186830117264 q^{41} - 160102538512 q^{42} + 147613206080 q^{43} + 146754773860 q^{44} + 167965018760 q^{45} + 33234006318 q^{46} + 136146541776 q^{47} - 918554738528 q^{48} - 279115649456 q^{49} + 446501048144 q^{50} + 374908120992 q^{51} + 920059547960 q^{52} - 365779470792 q^{53} + 142841959918 q^{54} - 335157159792 q^{55} - 2232488591424 q^{56} + 1368890666384 q^{57} + 1968765302052 q^{58} + 1211924963928 q^{59} - 1696452613604 q^{60} - 155263824184 q^{61} - 3267358992324 q^{62} - 4123328121080 q^{63} + 3671045348608 q^{64} + 2491203210104 q^{65} + 6785854381222 q^{66} - 1812819047992 q^{67} + 2300642770860 q^{68} - 9833331511584 q^{69} - 10764563120010 q^{70} + 6413635527072 q^{71} + 9182131417728 q^{72} + 7135229075576 q^{73} - 1240472589270 q^{74} + 3092701132528 q^{75} - 24098923346008 q^{76} - 8899938075392 q^{77} + 16977900019528 q^{78} + 7912090175960 q^{79} + 18767635478704 q^{80} - 2029193868592 q^{81} + 2118830761068 q^{82} - 16937841300576 q^{83} - 32302920082804 q^{84} + 9546866646768 q^{85} + 17052910238024 q^{86} + 16147535411672 q^{87} - 15433836932304 q^{88} + 3654589406888 q^{89} - 6354662390216 q^{90} - 14961004874704 q^{91} + 2966525661672 q^{92} + 10829807426472 q^{93} + 7135101410430 q^{94} - 16751540432680 q^{95} - 4043645970784 q^{96} + 20623672673744 q^{97} + 1374873929086 q^{98} + 1803523183088 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(7, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
7.14.c.a 7.c 7.c $16$ $7.506$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-2\) \(728\) \(46928\) \(257992\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(91\beta _{2}-\beta _{4})q^{3}+(-6\beta _{1}+\cdots)q^{4}+\cdots\)