Properties

Label 91.10.a
Level $91$
Weight $10$
Character orbit 91.a
Rep. character $\chi_{91}(1,\cdot)$
Character field $\Q$
Dimension $54$
Newform subspaces $4$
Sturm bound $93$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 91.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(93\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(91))\).

Total New Old
Modular forms 86 54 32
Cusp forms 82 54 28
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.
\(+\)\(+\)\(+\)\(13\)
\(+\)\(-\)\(-\)\(15\)
\(-\)\(+\)\(-\)\(14\)
\(-\)\(-\)\(+\)\(12\)
Plus space\(+\)\(25\)
Minus space\(-\)\(29\)

Trace form

\( 54 q + 2 q^{2} + 4 q^{3} + 15022 q^{4} - 3184 q^{5} - 6232 q^{6} - 4802 q^{7} + 9390 q^{8} + 477770 q^{9} + O(q^{10}) \) \( 54 q + 2 q^{2} + 4 q^{3} + 15022 q^{4} - 3184 q^{5} - 6232 q^{6} - 4802 q^{7} + 9390 q^{8} + 477770 q^{9} + 33552 q^{10} - 82288 q^{11} + 194840 q^{12} + 24010 q^{14} - 213920 q^{15} + 4280390 q^{16} - 881068 q^{17} - 1057946 q^{18} + 2304716 q^{19} + 1485556 q^{20} - 777924 q^{21} + 199972 q^{22} + 1227928 q^{23} + 518396 q^{24} + 21810478 q^{25} - 4012328 q^{27} - 10453954 q^{28} - 2502272 q^{29} - 35925864 q^{30} - 11629656 q^{31} + 11344362 q^{32} + 28077496 q^{33} - 52899480 q^{34} - 3102092 q^{35} + 239581610 q^{36} - 36735028 q^{37} - 117201512 q^{38} - 18507528 q^{39} + 176851868 q^{40} + 42705500 q^{41} - 30300620 q^{42} + 57237212 q^{43} - 1884924 q^{44} - 151242056 q^{45} - 51987072 q^{46} + 176215952 q^{47} + 214634532 q^{48} + 311299254 q^{49} - 57343874 q^{50} - 123690256 q^{51} + 104875992 q^{52} + 178950560 q^{53} - 8101600 q^{54} - 112784920 q^{55} + 63083874 q^{56} - 179825784 q^{57} - 357891832 q^{58} + 168727084 q^{59} - 570799844 q^{60} + 42785216 q^{61} - 103434584 q^{62} - 77970074 q^{63} + 501947462 q^{64} - 109445752 q^{65} + 1082341956 q^{66} + 975090680 q^{67} - 1111499592 q^{68} - 408588232 q^{69} + 210980672 q^{70} - 1286973896 q^{71} + 1184148950 q^{72} - 556343292 q^{73} + 1827246680 q^{74} - 148023364 q^{75} + 137138552 q^{76} + 206044216 q^{77} - 148060224 q^{78} + 2703107576 q^{79} - 2033394944 q^{80} + 5313827558 q^{81} - 226623236 q^{82} - 1678503900 q^{83} - 597445632 q^{84} - 1257329816 q^{85} - 1454072964 q^{86} + 2744212952 q^{87} + 104538612 q^{88} + 744081284 q^{89} - 3169039996 q^{90} - 274299844 q^{91} + 890641356 q^{92} - 4375496328 q^{93} - 3950390908 q^{94} + 2459638884 q^{95} + 4451658884 q^{96} - 394972852 q^{97} + 11529602 q^{98} - 5698278512 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(91))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 13
91.10.a.a \(12\) \(46.868\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-21\) \(-323\) \(-5202\) \(28812\) \(-\) \(-\) \(q+(-2+\beta _{1})q^{2}+(-3^{3}-\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
91.10.a.b \(13\) \(46.868\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-26\) \(163\) \(-2640\) \(-31213\) \(+\) \(+\) \(q+(-2+\beta _{1})q^{2}+(13-\beta _{5})q^{3}+(253+\cdots)q^{4}+\cdots\)
91.10.a.c \(14\) \(46.868\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(27\) \(163\) \(2964\) \(33614\) \(-\) \(+\) \(q+(2-\beta _{1})q^{2}+(12-\beta _{4})q^{3}+(171-6\beta _{1}+\cdots)q^{4}+\cdots\)
91.10.a.d \(15\) \(46.868\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(22\) \(1\) \(1694\) \(-36015\) \(+\) \(-\) \(q+(1+\beta _{1})q^{2}-\beta _{3}q^{3}+(427+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(91))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(91)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 2}\)