Properties

Label 93.4.a
Level $93$
Weight $4$
Character orbit 93.a
Rep. character $\chi_{93}(1,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $6$
Sturm bound $42$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 93 = 3 \cdot 31 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 93.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(42\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(93))\).

Total New Old
Modular forms 34 16 18
Cusp forms 30 16 14
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.

\(3\)\(31\)FrickeDim
\(+\)\(+\)$+$\(3\)
\(+\)\(-\)$-$\(5\)
\(-\)\(+\)$-$\(2\)
\(-\)\(-\)$+$\(6\)
Plus space\(+\)\(9\)
Minus space\(-\)\(7\)

Trace form

\( 16 q + 52 q^{4} + 20 q^{7} - 42 q^{8} + 144 q^{9} + O(q^{10}) \) \( 16 q + 52 q^{4} + 20 q^{7} - 42 q^{8} + 144 q^{9} + 78 q^{10} - 40 q^{11} + 24 q^{12} - 96 q^{13} - 222 q^{14} + 24 q^{15} + 180 q^{16} + 24 q^{17} + 32 q^{19} - 126 q^{20} - 212 q^{22} - 224 q^{23} + 180 q^{24} - 52 q^{25} + 268 q^{26} + 542 q^{28} + 24 q^{29} - 72 q^{30} + 186 q^{31} - 616 q^{32} - 60 q^{33} + 52 q^{34} - 1100 q^{35} + 468 q^{36} - 8 q^{37} - 718 q^{38} + 312 q^{39} + 612 q^{40} - 8 q^{41} + 240 q^{42} - 384 q^{43} + 160 q^{44} + 392 q^{46} - 532 q^{47} + 288 q^{48} + 2168 q^{49} + 22 q^{50} + 744 q^{51} - 1864 q^{52} - 80 q^{53} - 152 q^{55} - 2944 q^{56} + 384 q^{57} - 824 q^{58} - 584 q^{59} + 1188 q^{60} - 1000 q^{61} + 180 q^{63} + 290 q^{64} - 696 q^{65} + 384 q^{66} + 1372 q^{67} - 2612 q^{68} - 528 q^{69} + 1874 q^{70} + 1288 q^{71} - 378 q^{72} + 1720 q^{73} - 2056 q^{74} - 528 q^{75} + 2522 q^{76} + 1352 q^{77} - 852 q^{78} + 2016 q^{79} + 2850 q^{80} + 1296 q^{81} - 2906 q^{82} - 896 q^{83} - 2184 q^{84} - 2168 q^{85} + 5492 q^{86} + 564 q^{87} - 1364 q^{88} - 4376 q^{89} + 702 q^{90} + 2176 q^{91} + 1156 q^{92} + 186 q^{93} + 612 q^{94} + 1196 q^{95} - 1140 q^{96} - 3220 q^{97} + 4510 q^{98} - 360 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(93))\) 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 31
93.4.a.a 93.a 1.a $1$ $5.487$ \(\Q\) None \(3\) \(-3\) \(-9\) \(-34\) $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{2}-3q^{3}+q^{4}-9q^{5}-9q^{6}+\cdots\)
93.4.a.b 93.a 1.a $2$ $5.487$ \(\Q(\sqrt{29}) \) None \(-5\) \(-6\) \(8\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-2-\beta )q^{2}-3q^{3}+(3+5\beta )q^{4}+\cdots\)
93.4.a.c 93.a 1.a $2$ $5.487$ \(\Q(\sqrt{17}) \) None \(-3\) \(6\) \(-8\) \(-37\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+3q^{3}+(-3+3\beta )q^{4}+\cdots\)
93.4.a.d 93.a 1.a $2$ $5.487$ \(\Q(\sqrt{41}) \) None \(-1\) \(-6\) \(-11\) \(29\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-3q^{3}+(2+\beta )q^{4}+(-7+3\beta )q^{5}+\cdots\)
93.4.a.e 93.a 1.a $3$ $5.487$ 3.3.2089.1 None \(3\) \(-9\) \(8\) \(19\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}-3q^{3}+(1+3\beta _{1}+2\beta _{2})q^{4}+\cdots\)
93.4.a.f 93.a 1.a $6$ $5.487$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(3\) \(18\) \(12\) \(47\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+3q^{3}+(6+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(93))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(93)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 2}\)