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Properties

Label 2093.2.a
Level $2093$
Weight $2$
Character orbit 2093.a
Rep. character $\chi_{2093}(1,\cdot)$
Character field $\Q$
Dimension $131$
Newform subspaces $19$
Sturm bound $448$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 2093 = 7 \cdot 13 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2093.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 19 \)
Sturm bound: \(448\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2093))\).

Total New Old
Modular forms 228 131 97
Cusp forms 221 131 90
Eisenstein series 7 0 7

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

\(7\)\(13\)\(23\)FrickeDim
\(+\)\(+\)\(+\)$+$\(16\)
\(+\)\(+\)\(-\)$-$\(17\)
\(+\)\(-\)\(+\)$-$\(21\)
\(+\)\(-\)\(-\)$+$\(12\)
\(-\)\(+\)\(+\)$-$\(17\)
\(-\)\(+\)\(-\)$+$\(16\)
\(-\)\(-\)\(+\)$+$\(12\)
\(-\)\(-\)\(-\)$-$\(20\)
Plus space\(+\)\(56\)
Minus space\(-\)\(75\)

Trace form

\( 131 q + q^{2} + 4 q^{3} + 125 q^{4} - 6 q^{5} - 4 q^{6} - q^{7} - 3 q^{8} + 143 q^{9} + O(q^{10}) \) \( 131 q + q^{2} + 4 q^{3} + 125 q^{4} - 6 q^{5} - 4 q^{6} - q^{7} - 3 q^{8} + 143 q^{9} - 2 q^{10} - 4 q^{11} + 12 q^{12} - q^{13} - 3 q^{14} - 24 q^{15} + 117 q^{16} + 6 q^{17} + 37 q^{18} + 4 q^{19} + 14 q^{20} - 4 q^{21} + 4 q^{22} - q^{23} + 20 q^{24} + 101 q^{25} - 3 q^{26} - 8 q^{27} - 7 q^{28} - 30 q^{29} + 40 q^{30} - 16 q^{31} + 5 q^{32} + 48 q^{33} - 30 q^{34} - 6 q^{35} + 137 q^{36} - 22 q^{37} + 60 q^{38} + 12 q^{39} + 14 q^{40} + 22 q^{41} + 28 q^{42} + 36 q^{43} - 4 q^{44} - 78 q^{45} + 5 q^{46} - 24 q^{47} + 20 q^{48} + 131 q^{49} + 47 q^{50} + 8 q^{51} + 9 q^{52} - 46 q^{53} - 40 q^{54} + 8 q^{55} - 15 q^{56} + 32 q^{57} - 26 q^{58} + 12 q^{59} + 48 q^{60} - 6 q^{61} + 56 q^{62} - 13 q^{63} + 37 q^{64} - 6 q^{65} + 56 q^{66} + 4 q^{67} - 14 q^{68} - 4 q^{69} - 10 q^{70} + 24 q^{71} + 137 q^{72} + 14 q^{73} - 26 q^{74} + 108 q^{75} - 68 q^{76} - 12 q^{77} - 4 q^{78} - 48 q^{79} + 102 q^{80} + 171 q^{81} - 54 q^{82} + 4 q^{83} - 28 q^{84} - 36 q^{85} + 12 q^{86} + 56 q^{87} - 12 q^{88} - 10 q^{89} + 6 q^{90} - q^{91} - 7 q^{92} - 48 q^{93} + 72 q^{94} - 32 q^{95} - 84 q^{96} + 46 q^{97} + q^{98} - 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2093))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 7 13 23
2093.2.a.a 2093.a 1.a $1$ $16.713$ \(\Q\) None \(-2\) \(-1\) \(-3\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}-3q^{5}+2q^{6}+\cdots\)
2093.2.a.b 2093.a 1.a $1$ $16.713$ \(\Q\) None \(-2\) \(-1\) \(1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}+q^{7}+\cdots\)
2093.2.a.c 2093.a 1.a $1$ $16.713$ \(\Q\) None \(-2\) \(3\) \(3\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+2q^{4}+3q^{5}-6q^{6}+\cdots\)
2093.2.a.d 2093.a 1.a $1$ $16.713$ \(\Q\) None \(-1\) \(2\) \(0\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}-q^{4}-2q^{6}+q^{7}+3q^{8}+\cdots\)
2093.2.a.e 2093.a 1.a $1$ $16.713$ \(\Q\) None \(0\) \(-2\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{4}+q^{7}+q^{9}-3q^{11}+\cdots\)
2093.2.a.f 2093.a 1.a $1$ $16.713$ \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+q^{5}-q^{7}-2q^{9}+5q^{11}+\cdots\)
2093.2.a.g 2093.a 1.a $1$ $16.713$ \(\Q\) None \(0\) \(1\) \(-3\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-3q^{5}+q^{7}-2q^{9}+3q^{11}+\cdots\)
2093.2.a.h 2093.a 1.a $1$ $16.713$ \(\Q\) None \(0\) \(1\) \(3\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+3q^{5}+q^{7}-2q^{9}-3q^{11}+\cdots\)
2093.2.a.i 2093.a 1.a $1$ $16.713$ \(\Q\) None \(0\) \(2\) \(-4\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{4}-4q^{5}-q^{7}+q^{9}-5q^{11}+\cdots\)
2093.2.a.j 2093.a 1.a $1$ $16.713$ \(\Q\) None \(2\) \(2\) \(2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{3}+2q^{4}+2q^{5}+4q^{6}+\cdots\)
2093.2.a.k 2093.a 1.a $2$ $16.713$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1-\beta )q^{3}+(-1+2\beta )q^{5}+\cdots\)
2093.2.a.l 2093.a 1.a $6$ $16.713$ 6.6.52212317.1 None \(-1\) \(-5\) \(-2\) \(6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
2093.2.a.m 2093.a 1.a $11$ $16.713$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-1\) \(-3\) \(-4\) \(-11\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots\)
2093.2.a.n 2093.a 1.a $15$ $16.713$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(1\) \(-7\) \(-10\) \(15\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{11}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
2093.2.a.o 2093.a 1.a $16$ $16.713$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-3\) \(-4\) \(7\) \(-16\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots\)
2093.2.a.p 2093.a 1.a $16$ $16.713$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(3\) \(4\) \(3\) \(16\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}-\beta _{14}q^{5}+\cdots\)
2093.2.a.q 2093.a 1.a $16$ $16.713$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(6\) \(-1\) \(0\) \(-16\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{12}q^{3}+(1+\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots\)
2093.2.a.r 2093.a 1.a $19$ $16.713$ \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(-1\) \(8\) \(5\) \(19\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots\)
2093.2.a.s 2093.a 1.a $20$ $16.713$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(2\) \(8\) \(-3\) \(-20\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(2+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2093))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2093)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(299))\)\(^{\oplus 2}\)