Properties

Label 91.8.a
Level $91$
Weight $8$
Character orbit 91.a
Rep. character $\chi_{91}(1,\cdot)$
Character field $\Q$
Dimension $42$
Newform subspaces $5$
Sturm bound $74$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 91.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(74\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(91))\).

Total New Old
Modular forms 66 42 24
Cusp forms 62 42 20
Eisenstein series 4 0 4

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

\(7\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(11\)
\(+\)\(-\)\(-\)\(9\)
\(-\)\(+\)\(-\)\(10\)
\(-\)\(-\)\(+\)\(12\)
Plus space\(+\)\(23\)
Minus space\(-\)\(19\)

Trace form

\( 42 q + 2 q^{2} - 104 q^{3} + 2766 q^{4} + 284 q^{5} + 1160 q^{6} + 686 q^{7} + 1854 q^{8} + 28226 q^{9} + O(q^{10}) \) \( 42 q + 2 q^{2} - 104 q^{3} + 2766 q^{4} + 284 q^{5} + 1160 q^{6} + 686 q^{7} + 1854 q^{8} + 28226 q^{9} + 16592 q^{10} + 8720 q^{11} - 38632 q^{12} - 8918 q^{14} - 24332 q^{15} + 235078 q^{16} + 84968 q^{17} + 46966 q^{18} - 148032 q^{19} - 101708 q^{20} + 37044 q^{21} - 173580 q^{22} - 41222 q^{23} - 214948 q^{24} + 651012 q^{25} - 9308 q^{27} + 187278 q^{28} + 28690 q^{29} + 753432 q^{30} + 332172 q^{31} - 182406 q^{32} + 213244 q^{33} + 735752 q^{34} - 29498 q^{35} + 1405466 q^{36} - 518868 q^{37} + 2439736 q^{38} + 474552 q^{39} + 270076 q^{40} - 2220640 q^{41} - 1159340 q^{42} + 86602 q^{43} - 732588 q^{44} + 1012312 q^{45} - 2816800 q^{46} + 2479160 q^{47} - 539196 q^{48} + 4941258 q^{49} - 3853778 q^{50} + 3453632 q^{51} - 17576 q^{52} - 6441670 q^{53} + 770912 q^{54} + 143252 q^{55} - 3825822 q^{56} + 3095520 q^{57} + 1052120 q^{58} - 7595516 q^{59} + 13075132 q^{60} + 2469844 q^{61} + 2024392 q^{62} + 275086 q^{63} + 24091910 q^{64} + 3088982 q^{65} - 28577340 q^{66} + 6279932 q^{67} + 16479288 q^{68} - 6618916 q^{69} + 5345312 q^{70} + 6295576 q^{71} - 5562922 q^{72} + 15689112 q^{73} - 8221240 q^{74} - 24656572 q^{75} - 18456776 q^{76} + 5957224 q^{77} + 1898208 q^{78} - 17145094 q^{79} - 4698848 q^{80} + 27713954 q^{81} - 4043844 q^{82} - 13995180 q^{83} + 7112448 q^{84} - 4188772 q^{85} + 48129228 q^{86} - 25649992 q^{87} - 11289852 q^{88} - 40806184 q^{89} + 76101764 q^{90} + 3014284 q^{91} - 36005460 q^{92} + 5275356 q^{93} + 28350276 q^{94} - 2746986 q^{95} - 17676508 q^{96} - 5641728 q^{97} + 235298 q^{98} + 29659252 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(91))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 13
91.8.a.a \(1\) \(28.427\) \(\Q\) None \(22\) \(21\) \(140\) \(-343\) \(+\) \(+\) \(q+22q^{2}+21q^{3}+356q^{4}+140q^{5}+\cdots\)
91.8.a.b \(9\) \(28.427\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-5\) \(-26\) \(-181\) \(-3087\) \(+\) \(-\) \(q+(-1+\beta _{1})q^{2}+(-3+\beta _{2})q^{3}+(43+\cdots)q^{4}+\cdots\)
91.8.a.c \(10\) \(28.427\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-18\) \(-80\) \(-927\) \(3430\) \(-\) \(+\) \(q+(-2+\beta _{1})q^{2}+(-8-\beta _{1}+\beta _{3})q^{3}+\cdots\)
91.8.a.d \(10\) \(28.427\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-3\) \(-101\) \(226\) \(-3430\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(-10-\beta _{1}-\beta _{3})q^{3}+(6^{2}+\cdots)q^{4}+\cdots\)
91.8.a.e \(12\) \(28.427\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(82\) \(1026\) \(4116\) \(-\) \(-\) \(q+(1-\beta _{1})q^{2}+(7+\beta _{3})q^{3}+(82+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(91))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(91)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 2}\)