Properties

Label 99.14.a
Level $99$
Weight $14$
Character orbit 99.a
Rep. character $\chi_{99}(1,\cdot)$
Character field $\Q$
Dimension $54$
Newform subspaces $9$
Sturm bound $168$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 99.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(168\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(99))\).

Total New Old
Modular forms 160 54 106
Cusp forms 152 54 98
Eisenstein series 8 0 8

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

\(3\)\(11\)FrickeDim
\(+\)\(+\)$+$\(11\)
\(+\)\(-\)$-$\(11\)
\(-\)\(+\)$-$\(17\)
\(-\)\(-\)$+$\(15\)
Plus space\(+\)\(26\)
Minus space\(-\)\(28\)

Trace form

\( 54 q - 64 q^{2} + 233836 q^{4} + 31493 q^{5} + 27662 q^{7} - 2891040 q^{8} + O(q^{10}) \) \( 54 q - 64 q^{2} + 233836 q^{4} + 31493 q^{5} + 27662 q^{7} - 2891040 q^{8} - 1451762 q^{10} - 3543122 q^{11} + 48416210 q^{13} - 190402048 q^{14} + 974001472 q^{16} - 198625480 q^{17} - 97895564 q^{19} + 1020291148 q^{20} + 113379904 q^{22} + 833603017 q^{23} + 11500936855 q^{25} - 2959607752 q^{26} - 1497416736 q^{28} - 3399284550 q^{29} + 12671006423 q^{31} - 7037140724 q^{32} + 22551921544 q^{34} - 35626107574 q^{35} - 24571209503 q^{37} + 2709892200 q^{38} - 66334813308 q^{40} + 102937615454 q^{41} - 37121151722 q^{43} + 15114958452 q^{44} + 33350176094 q^{46} - 160818966488 q^{47} + 455020708866 q^{49} + 520995307318 q^{50} - 144092206608 q^{52} - 349803538068 q^{53} + 94146066223 q^{55} - 1564885448508 q^{56} - 335109891492 q^{58} - 1537442962265 q^{59} + 478016438650 q^{61} + 971991721250 q^{62} + 3428736725472 q^{64} + 2226427424768 q^{65} + 431605835949 q^{67} + 211655713504 q^{68} + 1443118699780 q^{70} - 715775792109 q^{71} + 1638877709558 q^{73} + 7352976110238 q^{74} - 1332893995544 q^{76} - 1269603363138 q^{77} + 9203307586350 q^{79} + 4475257827532 q^{80} + 12444973360540 q^{82} + 11362431667386 q^{83} - 19352827082822 q^{85} - 14328658016676 q^{86} + 3362599934100 q^{88} + 11996135192739 q^{89} - 7696788096936 q^{91} - 13855046920348 q^{92} - 52927361134072 q^{94} + 44891626422192 q^{95} + 8899483836075 q^{97} - 31985147963688 q^{98} + O(q^{100}) \)

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(99))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 11
99.14.a.a 99.a 1.a $1$ $106.159$ \(\Q\) None \(-140\) \(0\) \(-48740\) \(487486\) $-$ $-$ $\mathrm{SU}(2)$ \(q-140q^{2}+11408q^{4}-48740q^{5}+\cdots\)
99.14.a.b 99.a 1.a $4$ $106.159$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-41\) \(0\) \(38422\) \(41998\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-10-\beta _{1})q^{2}+(5909+43\beta _{1}+5\beta _{3})q^{4}+\cdots\)
99.14.a.c 99.a 1.a $4$ $106.159$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(11\) \(0\) \(83432\) \(69652\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(3-\beta _{1})q^{2}+(-1564+37\beta _{1}+5\beta _{2}+\cdots)q^{4}+\cdots\)
99.14.a.d 99.a 1.a $5$ $106.159$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(53\) \(0\) \(-10318\) \(-667804\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(11-\beta _{1})q^{2}+(7020-11\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
99.14.a.e 99.a 1.a $5$ $106.159$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(64\) \(0\) \(454\) \(-313920\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(13+\beta _{1})q^{2}+(-477+21\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
99.14.a.f 99.a 1.a $6$ $106.159$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-11\) \(0\) \(20932\) \(284152\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{2}+(3061-10\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
99.14.a.g 99.a 1.a $7$ $106.159$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(0\) \(-52689\) \(-89386\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(6727+6\beta _{1}+\beta _{2})q^{4}+(-7527+\cdots)q^{5}+\cdots\)
99.14.a.h 99.a 1.a $11$ $106.159$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-64\) \(0\) \(-62500\) \(107742\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-6+\beta _{1})q^{2}+(4859-11\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
99.14.a.i 99.a 1.a $11$ $106.159$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(64\) \(0\) \(62500\) \(107742\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(6-\beta _{1})q^{2}+(4859-11\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(99))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_0(99)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 2}\)