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Properties

Label 98.14.c
Level $98$
Weight $14$
Character orbit 98.c
Rep. character $\chi_{98}(67,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $88$
Newform subspaces $18$
Sturm bound $196$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 98.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 18 \)
Sturm bound: \(196\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(98, [\chi])\).

Total New Old
Modular forms 380 88 292
Cusp forms 348 88 260
Eisenstein series 32 0 32

Trace form

\( 88 q - 180224 q^{4} + 62608 q^{5} - 46592 q^{6} - 25479048 q^{9} + O(q^{10}) \) \( 88 q - 180224 q^{4} + 62608 q^{5} - 46592 q^{6} - 25479048 q^{9} + 4236288 q^{10} + 17549436 q^{11} - 55245680 q^{13} + 430947040 q^{15} - 738197504 q^{16} + 173276096 q^{17} + 446870272 q^{18} + 639112600 q^{19} - 512884736 q^{20} + 1860481024 q^{22} - 707667880 q^{23} + 95420416 q^{24} - 10960253148 q^{25} + 1675803136 q^{26} + 13674585456 q^{27} - 25538117984 q^{29} + 1156757760 q^{30} - 7620869816 q^{31} - 8347025624 q^{33} - 20145914880 q^{34} + 208724361216 q^{36} - 25277013872 q^{37} + 13292735232 q^{38} + 107031382520 q^{39} + 17351835648 q^{40} - 200030490576 q^{41} + 424664866184 q^{43} + 71882489856 q^{44} + 224768920936 q^{45} - 63519486208 q^{46} + 84492403800 q^{47} - 255475862528 q^{50} + 271798853756 q^{51} + 113143152640 q^{52} + 27483564720 q^{53} - 228393530624 q^{54} - 876549420096 q^{55} + 763117936488 q^{57} + 461482996736 q^{58} + 1060437579040 q^{59} - 882579537920 q^{60} + 302092281064 q^{61} - 589655209472 q^{62} + 6047313952768 q^{64} + 1398345557224 q^{65} + 2695993323520 q^{66} + 896663713392 q^{67} + 709738889216 q^{68} - 9547459848416 q^{69} + 3853602549584 q^{71} + 1830380634112 q^{72} + 6459088113352 q^{73} + 1126781095936 q^{74} + 3701297994800 q^{75} - 5235610419200 q^{76} + 11987616305152 q^{78} + 14309911029704 q^{79} + 1050387939328 q^{80} - 26144836783840 q^{81} + 872746581504 q^{82} - 3647678607328 q^{83} - 4533958394176 q^{85} + 721370500864 q^{86} + 14980266985544 q^{87} - 3810265137152 q^{88} - 1552477239432 q^{89} - 1899518028800 q^{90} + 5797215272960 q^{92} + 5550450039040 q^{93} + 5005439894784 q^{94} - 25442997242440 q^{95} + 390842023936 q^{96} - 9790396414064 q^{97} + 32870844990232 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(98, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
98.14.c.a 98.c 7.c $2$ $105.086$ \(\Q(\sqrt{-3}) \) None \(-64\) \(-1236\) \(57450\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2^{6}\zeta_{6}q^{2}+(-1236+1236\zeta_{6})q^{3}+\cdots\)
98.14.c.b 98.c 7.c $2$ $105.086$ \(\Q(\sqrt{-3}) \) None \(-64\) \(-1026\) \(4320\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2^{6}\zeta_{6}q^{2}+(-1026+1026\zeta_{6})q^{3}+\cdots\)
98.14.c.c 98.c 7.c $2$ $105.086$ \(\Q(\sqrt{-3}) \) None \(-64\) \(1026\) \(-4320\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2^{6}\zeta_{6}q^{2}+(1026-1026\zeta_{6})q^{3}+\cdots\)
98.14.c.d 98.c 7.c $2$ $105.086$ \(\Q(\sqrt{-3}) \) None \(-64\) \(1236\) \(-57450\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2^{6}\zeta_{6}q^{2}+(1236-1236\zeta_{6})q^{3}+\cdots\)
98.14.c.e 98.c 7.c $2$ $105.086$ \(\Q(\sqrt{-3}) \) None \(64\) \(-1836\) \(3990\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2^{6}\zeta_{6}q^{2}+(-1836+1836\zeta_{6})q^{3}+\cdots\)
98.14.c.f 98.c 7.c $2$ $105.086$ \(\Q(\sqrt{-3}) \) None \(64\) \(-1626\) \(36400\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2^{6}\zeta_{6}q^{2}+(-1626+1626\zeta_{6})q^{3}+\cdots\)
98.14.c.g 98.c 7.c $2$ $105.086$ \(\Q(\sqrt{-3}) \) None \(64\) \(1626\) \(-36400\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2^{6}\zeta_{6}q^{2}+(1626-1626\zeta_{6})q^{3}+\cdots\)
98.14.c.h 98.c 7.c $2$ $105.086$ \(\Q(\sqrt{-3}) \) None \(64\) \(1836\) \(-3990\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2^{6}\zeta_{6}q^{2}+(1836-1836\zeta_{6})q^{3}+\cdots\)
98.14.c.i 98.c 7.c $4$ $105.086$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-128\) \(-1106\) \(-75530\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2^{6}\beta _{1}q^{2}+(-553+553\beta _{1}-5\beta _{2}+\cdots)q^{3}+\cdots\)
98.14.c.j 98.c 7.c $4$ $105.086$ \(\Q(\sqrt{-3}, \sqrt{373})\) None \(-128\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2^{6}+2^{6}\beta _{1})q^{2}-3\beta _{2}q^{3}-2^{12}\beta _{1}q^{4}+\cdots\)
98.14.c.k 98.c 7.c $4$ $105.086$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-128\) \(1106\) \(75530\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2^{6}\beta _{1}q^{2}+(553-553\beta _{1}+5\beta _{2}+\cdots)q^{3}+\cdots\)
98.14.c.l 98.c 7.c $4$ $105.086$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(128\) \(-952\) \(-32004\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2^{6}-2^{6}\beta _{1})q^{2}+(-476\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
98.14.c.m 98.c 7.c $4$ $105.086$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(128\) \(952\) \(32004\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2^{6}-2^{6}\beta _{1})q^{2}+(476\beta _{1}+\beta _{2})q^{3}+\cdots\)
98.14.c.n 98.c 7.c $8$ $105.086$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-256\) \(182\) \(64400\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2^{6}-2^{6}\beta _{1})q^{2}+(-45\beta _{1}+\beta _{4}+\cdots)q^{3}+\cdots\)
98.14.c.o 98.c 7.c $8$ $105.086$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(256\) \(-182\) \(-1792\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2^{6}-2^{6}\beta _{1})q^{2}+(-46\beta _{1}-\beta _{2})q^{3}+\cdots\)
98.14.c.p 98.c 7.c $8$ $105.086$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(256\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2^{6}\beta _{1}q^{2}+(-\beta _{2}+\beta _{3})q^{3}+(-2^{12}+\cdots)q^{4}+\cdots\)
98.14.c.q 98.c 7.c $12$ $105.086$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(384\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2^{6}-2^{6}\beta _{1})q^{2}+(-\beta _{8}+8\beta _{9})q^{3}+\cdots\)
98.14.c.r 98.c 7.c $16$ $105.086$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-512\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2^{6}\beta _{1}q^{2}+\beta _{3}q^{3}+(-2^{12}+2^{12}\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{14}^{\mathrm{old}}(98, [\chi])\) into lower level spaces

\( S_{14}^{\mathrm{old}}(98, [\chi]) \cong \) \(S_{14}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)