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Properties

Label 98.14.a
Level $98$
Weight $14$
Character orbit 98.a
Rep. character $\chi_{98}(1,\cdot)$
Character field $\Q$
Dimension $44$
Newform subspaces $14$
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.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 14 \)
Sturm bound: \(196\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(98))\).

Total New Old
Modular forms 190 44 146
Cusp forms 174 44 130
Eisenstein series 16 0 16

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(7\)FrickeDim
\(+\)\(+\)$+$\(10\)
\(+\)\(-\)$-$\(12\)
\(-\)\(+\)$-$\(12\)
\(-\)\(-\)$+$\(10\)
Plus space\(+\)\(20\)
Minus space\(-\)\(24\)

Trace form

\( 44 q - 2058 q^{3} + 180224 q^{4} - 21994 q^{5} - 36736 q^{6} + 27207348 q^{9} + O(q^{10}) \) \( 44 q - 2058 q^{3} + 180224 q^{4} - 21994 q^{5} - 36736 q^{6} + 27207348 q^{9} - 1459584 q^{10} - 7699176 q^{11} - 8429568 q^{12} + 24382610 q^{13} + 106273856 q^{15} + 738197504 q^{16} - 259385588 q^{17} - 145346560 q^{18} - 249495022 q^{19} - 90087424 q^{20} + 811269632 q^{22} - 307823408 q^{23} - 150470656 q^{24} + 11081608536 q^{25} - 998558848 q^{26} - 605535084 q^{27} - 11083693492 q^{29} + 510269952 q^{30} + 14121263828 q^{31} + 3961341440 q^{33} + 2283020544 q^{34} + 111441297408 q^{36} + 77461171436 q^{37} - 3325381248 q^{38} - 65550518480 q^{39} - 5978456064 q^{40} - 11284926156 q^{41} + 79252652440 q^{43} - 31535824896 q^{44} - 73351391218 q^{45} + 83233928704 q^{46} - 276976755636 q^{47} - 34527510528 q^{48} - 270800392960 q^{50} + 247182942640 q^{51} + 99871170560 q^{52} + 89605852200 q^{53} - 409496512768 q^{54} - 182495167176 q^{55} - 1596325036944 q^{57} + 647573723392 q^{58} + 900178243202 q^{59} + 435297714176 q^{60} - 2320587225754 q^{61} - 214230214912 q^{62} + 3023656976384 q^{64} + 4119938130308 q^{65} + 1469556236288 q^{66} + 505230282264 q^{67} - 1062443368448 q^{68} - 1321410498352 q^{69} - 962689652720 q^{71} - 595339509760 q^{72} + 1654017867656 q^{73} + 3718502834432 q^{74} - 11082302285390 q^{75} - 1021931610112 q^{76} + 559277920256 q^{78} - 824757897008 q^{79} - 368998088704 q^{80} + 33727629257404 q^{81} - 4319590093056 q^{82} - 4663944932822 q^{83} - 20471969087084 q^{85} + 29407118336 q^{86} + 5530905893548 q^{87} + 3322960412672 q^{88} - 17740786060032 q^{89} - 6490043421568 q^{90} - 1260844679168 q^{92} + 28419910826240 q^{93} + 10202185496832 q^{94} - 1913744624336 q^{95} - 616327806976 q^{96} + 6222038154668 q^{97} + 23878919787536 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(98))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 7
98.14.a.a 98.a 1.a $1$ $105.086$ \(\Q\) None \(-64\) \(-1626\) \(36400\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{6}q^{2}-1626q^{3}+2^{12}q^{4}+36400q^{5}+\cdots\)
98.14.a.b 98.a 1.a $1$ $105.086$ \(\Q\) None \(-64\) \(1836\) \(-3990\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{6}q^{2}+1836q^{3}+2^{12}q^{4}-3990q^{5}+\cdots\)
98.14.a.c 98.a 1.a $1$ $105.086$ \(\Q\) None \(64\) \(-1236\) \(57450\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{6}q^{2}-1236q^{3}+2^{12}q^{4}+57450q^{5}+\cdots\)
98.14.a.d 98.a 1.a $1$ $105.086$ \(\Q\) None \(64\) \(1026\) \(-4320\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{6}q^{2}+1026q^{3}+2^{12}q^{4}-4320q^{5}+\cdots\)
98.14.a.e 98.a 1.a $2$ $105.086$ \(\Q(\sqrt{100129}) \) None \(-128\) \(-952\) \(-32004\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{6}q^{2}+(-476-\beta )q^{3}+2^{12}q^{4}+\cdots\)
98.14.a.f 98.a 1.a $2$ $105.086$ \(\Q(\sqrt{78985}) \) None \(128\) \(-1106\) \(-75530\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{6}q^{2}+(-553-5\beta )q^{3}+2^{12}q^{4}+\cdots\)
98.14.a.g 98.a 1.a $2$ $105.086$ \(\Q(\sqrt{373}) \) None \(128\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{6}q^{2}-3\beta q^{3}+2^{12}q^{4}-85\beta q^{5}+\cdots\)
98.14.a.h 98.a 1.a $4$ $105.086$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-256\) \(-182\) \(-1792\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{6}q^{2}+(-46+\beta _{1})q^{3}+2^{12}q^{4}+\cdots\)
98.14.a.i 98.a 1.a $4$ $105.086$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-256\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{6}q^{2}+\beta _{1}q^{3}+2^{12}q^{4}+(13\beta _{1}+\cdots)q^{5}+\cdots\)
98.14.a.j 98.a 1.a $4$ $105.086$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-256\) \(182\) \(1792\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{6}q^{2}+(46-\beta _{1})q^{3}+2^{12}q^{4}+(442+\cdots)q^{5}+\cdots\)
98.14.a.k 98.a 1.a $4$ $105.086$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(256\) \(-182\) \(-64400\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{6}q^{2}+(-45+\beta _{1})q^{3}+2^{12}q^{4}+\cdots\)
98.14.a.l 98.a 1.a $4$ $105.086$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(256\) \(182\) \(64400\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{6}q^{2}+(45-\beta _{1})q^{3}+2^{12}q^{4}+(16103+\cdots)q^{5}+\cdots\)
98.14.a.m 98.a 1.a $6$ $105.086$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-384\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{6}q^{2}+(\beta _{1}-8\beta _{2})q^{3}+2^{12}q^{4}+\cdots\)
98.14.a.n 98.a 1.a $8$ $105.086$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(512\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{6}q^{2}-\beta _{3}q^{3}+2^{12}q^{4}+(-19\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(98))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_0(98)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 2}\)