Properties

Label 2169.2.a
Level $2169$
Weight $2$
Character orbit 2169.a
Rep. character $\chi_{2169}(1,\cdot)$
Character field $\Q$
Dimension $100$
Newform subspaces $11$
Sturm bound $484$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 2169 = 3^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2169.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(484\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2169))\).

Total New Old
Modular forms 246 100 146
Cusp forms 239 100 139
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.

\(3\)\(241\)FrickeDim.
\(+\)\(+\)\(+\)\(14\)
\(+\)\(-\)\(-\)\(26\)
\(-\)\(+\)\(-\)\(33\)
\(-\)\(-\)\(+\)\(27\)
Plus space\(+\)\(41\)
Minus space\(-\)\(59\)

Trace form

\( 100q + 2q^{2} + 102q^{4} + 4q^{7} + 6q^{8} + O(q^{10}) \) \( 100q + 2q^{2} + 102q^{4} + 4q^{7} + 6q^{8} - 2q^{10} + 16q^{14} + 106q^{16} + 4q^{17} - 6q^{22} + 2q^{23} + 96q^{25} - 14q^{26} + 14q^{28} + 12q^{29} + 22q^{31} + 34q^{32} - 2q^{34} + 10q^{35} + 6q^{37} + 26q^{38} - 28q^{40} + 10q^{41} - 8q^{43} - 6q^{44} + 18q^{46} + 12q^{47} + 94q^{49} + 46q^{50} + 36q^{52} - 18q^{53} - 14q^{55} + 54q^{56} - 14q^{58} + 4q^{59} - 8q^{61} - 4q^{62} + 126q^{64} - 40q^{65} - 28q^{67} - 36q^{70} - 12q^{71} - 12q^{73} - 66q^{74} - 44q^{76} + 38q^{77} + 18q^{79} - 10q^{80} - 22q^{82} + 12q^{83} - 18q^{85} + 46q^{86} - 14q^{88} + 10q^{89} + 16q^{91} + 50q^{92} - 16q^{94} - 24q^{95} + 6q^{97} - 76q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2169))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 241
2169.2.a.a \(1\) \(17.320\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(q-2q^{4}-2q^{7}+q^{11}+4q^{16}+2q^{17}+\cdots\)
2169.2.a.b \(1\) \(17.320\) \(\Q\) None \(1\) \(0\) \(2\) \(0\) \(-\) \(+\) \(q+q^{2}-q^{4}+2q^{5}-3q^{8}+2q^{10}+\cdots\)
2169.2.a.c \(2\) \(17.320\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-4\) \(2\) \(-\) \(+\) \(q-q^{2}-q^{4}-2q^{5}+(1+\beta )q^{7}+3q^{8}+\cdots\)
2169.2.a.d \(5\) \(17.320\) 5.5.24217.1 None \(2\) \(0\) \(8\) \(-7\) \(-\) \(-\) \(q+(\beta _{1}+\beta _{2}-\beta _{4})q^{2}-\beta _{4}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
2169.2.a.e \(7\) \(17.320\) 7.7.31056073.1 None \(4\) \(0\) \(8\) \(-7\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\)
2169.2.a.f \(9\) \(17.320\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-3\) \(0\) \(-12\) \(-5\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{8})q^{5}+\cdots\)
2169.2.a.g \(10\) \(17.320\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(4\) \(0\) \(10\) \(3\) \(-\) \(+\) \(q-\beta _{9}q^{2}+(1+\beta _{7}-\beta _{9})q^{4}+(\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
2169.2.a.h \(12\) \(17.320\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(0\) \(-6\) \(3\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{9})q^{5}+\cdots\)
2169.2.a.i \(13\) \(17.320\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-1\) \(0\) \(-6\) \(9\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{7}q^{5}+(1+\beta _{11}+\cdots)q^{7}+\cdots\)
2169.2.a.j \(14\) \(17.320\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(0\) \(-14\) \(+\) \(+\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{12}q^{5}+(-1-\beta _{8}+\cdots)q^{7}+\cdots\)
2169.2.a.k \(26\) \(17.320\) None \(0\) \(0\) \(0\) \(22\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2169))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2169)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(241))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(723))\)\(^{\oplus 2}\)