Properties

Label 950.2.a
Level $950$
Weight $2$
Character orbit 950.a
Rep. character $\chi_{950}(1,\cdot)$
Character field $\Q$
Dimension $29$
Newform subspaces $14$
Sturm bound $300$
Trace bound $9$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 14 \)
Sturm bound: \(300\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(950))\).

Total New Old
Modular forms 162 29 133
Cusp forms 139 29 110
Eisenstein series 23 0 23

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

\(2\)\(5\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(5\)
\(+\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(6\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(6\)
Plus space\(+\)\(7\)
Minus space\(-\)\(22\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(950))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 19
950.2.a.a \(1\) \(7.586\) \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
950.2.a.b \(1\) \(7.586\) \(\Q\) None \(-1\) \(1\) \(0\) \(-3\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots\)
950.2.a.c \(1\) \(7.586\) \(\Q\) None \(-1\) \(3\) \(0\) \(5\) \(+\) \(+\) \(-\) \(q-q^{2}+3q^{3}+q^{4}-3q^{6}+5q^{7}-q^{8}+\cdots\)
950.2.a.d \(1\) \(7.586\) \(\Q\) None \(1\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
950.2.a.e \(1\) \(7.586\) \(\Q\) None \(1\) \(1\) \(0\) \(1\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
950.2.a.f \(2\) \(7.586\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(0\) \(6\) \(+\) \(-\) \(+\) \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots\)
950.2.a.g \(2\) \(7.586\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(0\) \(-6\) \(-\) \(-\) \(+\) \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
950.2.a.h \(2\) \(7.586\) \(\Q(\sqrt{17}) \) None \(2\) \(1\) \(0\) \(1\) \(-\) \(+\) \(+\) \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+\beta q^{7}+q^{8}+\cdots\)
950.2.a.i \(3\) \(7.586\) 3.3.568.1 None \(-3\) \(-2\) \(0\) \(-4\) \(+\) \(-\) \(-\) \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.a.j \(3\) \(7.586\) 3.3.993.1 None \(-3\) \(-2\) \(0\) \(-2\) \(+\) \(+\) \(-\) \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.a.k \(3\) \(7.586\) 3.3.257.1 None \(-3\) \(-2\) \(0\) \(-2\) \(+\) \(-\) \(+\) \(q-q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+(1+\cdots)q^{6}+\cdots\)
950.2.a.l \(3\) \(7.586\) 3.3.993.1 None \(3\) \(2\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1})q^{6}+\cdots\)
950.2.a.m \(3\) \(7.586\) 3.3.257.1 None \(3\) \(2\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q+q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.a.n \(3\) \(7.586\) 3.3.568.1 None \(3\) \(2\) \(0\) \(4\) \(-\) \(-\) \(-\) \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1})q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(950))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(950)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(475))\)\(^{\oplus 2}\)