Properties

Label 2151.2.a
Level $2151$
Weight $2$
Character orbit 2151.a
Rep. character $\chi_{2151}(1,\cdot)$
Character field $\Q$
Dimension $99$
Newform subspaces $11$
Sturm bound $480$
Trace bound $5$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2151.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(480\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2151))\).

Total New Old
Modular forms 244 99 145
Cusp forms 237 99 138
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.

\(3\)\(239\)FrickeDim.
\(+\)\(+\)\(+\)\(20\)
\(+\)\(-\)\(-\)\(20\)
\(-\)\(+\)\(-\)\(37\)
\(-\)\(-\)\(+\)\(22\)
Plus space\(+\)\(42\)
Minus space\(-\)\(57\)

Trace form

\( 99q + 94q^{4} - 6q^{7} + 6q^{8} + O(q^{10}) \) \( 99q + 94q^{4} - 6q^{7} + 6q^{8} + 2q^{10} - 2q^{11} - 6q^{13} + 14q^{14} + 92q^{16} - 6q^{19} - 4q^{20} - 8q^{22} + 2q^{23} + 99q^{25} + 14q^{26} - 22q^{28} - 4q^{29} - 4q^{31} + 22q^{32} + 10q^{34} + 28q^{35} - 6q^{37} + 12q^{40} - 6q^{41} + 16q^{43} + 14q^{44} - 4q^{46} + 16q^{47} + 89q^{49} + 22q^{50} - 36q^{52} - 4q^{55} + 36q^{56} + 20q^{59} + 8q^{61} + 15q^{62} + 74q^{64} + 48q^{65} + 12q^{67} + 8q^{68} + 32q^{70} + 4q^{71} + 28q^{73} + 24q^{74} - 64q^{76} - 10q^{77} - 20q^{79} - 17q^{80} - 10q^{82} + 12q^{83} + 8q^{85} - 28q^{86} - 40q^{88} + 18q^{89} - 26q^{91} - 12q^{92} - 58q^{94} + 14q^{95} - 2q^{97} - 42q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2151))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 239
2151.2.a.a \(2\) \(17.176\) \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(0\) \(0\) \(-\) \(-\) \(q+(-1-\beta )q^{2}+3\beta q^{4}+(-1+2\beta )q^{5}+\cdots\)
2151.2.a.b \(2\) \(17.176\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(-6\) \(2\) \(-\) \(-\) \(q-\beta q^{2}+(-1+\beta )q^{4}-3q^{5}+(2-2\beta )q^{7}+\cdots\)
2151.2.a.c \(2\) \(17.176\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(2\) \(0\) \(-\) \(-\) \(q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-1+2\beta )q^{8}+\cdots\)
2151.2.a.d \(3\) \(17.176\) \(\Q(\zeta_{14})^+\) None \(1\) \(0\) \(4\) \(-3\) \(-\) \(-\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{2})q^{5}-q^{7}+\cdots\)
2151.2.a.e \(6\) \(17.176\) 6.6.1767625.1 None \(2\) \(0\) \(-5\) \(-9\) \(-\) \(-\) \(q-\beta _{5}q^{2}+(1+\beta _{2}+\beta _{3}-\beta _{4})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
2151.2.a.f \(7\) \(17.176\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(0\) \(-3\) \(3\) \(-\) \(-\) \(q+\beta _{2}q^{2}+(1+\beta _{6})q^{4}-\beta _{6}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
2151.2.a.g \(8\) \(17.176\) 8.8.2585660609.1 None \(5\) \(0\) \(13\) \(-7\) \(-\) \(+\) \(q+(1+\beta _{2})q^{2}+(1+\beta _{2}+\beta _{3})q^{4}+(2+\cdots)q^{5}+\cdots\)
2151.2.a.h \(12\) \(17.176\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(0\) \(1\) \(11\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{9}q^{5}+(1+\beta _{8}+\cdots)q^{7}+\cdots\)
2151.2.a.i \(17\) \(17.176\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(0\) \(0\) \(-6\) \(5\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{13}q^{5}+(1+\cdots)q^{7}+\cdots\)
2151.2.a.j \(20\) \(17.176\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-4\) \(0\) \(-16\) \(-4\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{9})q^{5}+\cdots\)
2151.2.a.k \(20\) \(17.176\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(4\) \(0\) \(16\) \(-4\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{9})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2151))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2151)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(239))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(717))\)\(^{\oplus 2}\)