Properties

Label 1950.2.a
Level $1950$
Weight $2$
Character orbit 1950.a
Rep. character $\chi_{1950}(1,\cdot)$
Character field $\Q$
Dimension $38$
Newform subspaces $33$
Sturm bound $840$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 33 \)
Sturm bound: \(840\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\), \(23\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1950))\).

Total New Old
Modular forms 444 38 406
Cusp forms 397 38 359
Eisenstein series 47 0 47

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

\(2\)\(3\)\(5\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(1\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(4\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(14\)
Minus space\(-\)\(24\)

Trace form

\( 38q + 38q^{4} - 2q^{6} - 12q^{7} + 38q^{9} + O(q^{10}) \) \( 38q + 38q^{4} - 2q^{6} - 12q^{7} + 38q^{9} - 8q^{11} + 2q^{13} + 4q^{14} + 38q^{16} + 4q^{17} + 4q^{19} - 4q^{21} - 8q^{22} - 8q^{23} - 2q^{24} - 12q^{28} - 12q^{29} - 12q^{31} + 8q^{33} + 38q^{36} + 20q^{37} - 4q^{38} + 4q^{42} - 16q^{43} - 8q^{44} - 8q^{46} + 8q^{47} + 30q^{49} + 2q^{52} + 28q^{53} - 2q^{54} + 4q^{56} - 20q^{57} + 16q^{58} - 4q^{61} + 4q^{62} - 12q^{63} + 38q^{64} + 8q^{66} + 20q^{67} + 4q^{68} + 8q^{69} - 32q^{71} + 20q^{73} + 8q^{74} + 4q^{76} + 48q^{77} + 2q^{78} - 16q^{79} + 38q^{81} + 20q^{82} - 4q^{84} - 24q^{86} + 16q^{87} - 8q^{88} + 24q^{89} - 12q^{91} - 8q^{92} - 12q^{93} + 8q^{94} - 2q^{96} + 20q^{97} + 16q^{98} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1950))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5 13
1950.2.a.a \(1\) \(15.571\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-3\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-3q^{7}-q^{8}+\cdots\)
1950.2.a.b \(1\) \(15.571\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\)
1950.2.a.c \(1\) \(15.571\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\)
1950.2.a.d \(1\) \(15.571\) \(\Q\) None \(-1\) \(-1\) \(0\) \(4\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+4q^{7}-q^{8}+\cdots\)
1950.2.a.e \(1\) \(15.571\) \(\Q\) None \(-1\) \(-1\) \(0\) \(4\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+4q^{7}-q^{8}+\cdots\)
1950.2.a.f \(1\) \(15.571\) \(\Q\) None \(-1\) \(1\) \(0\) \(-4\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-4q^{7}-q^{8}+\cdots\)
1950.2.a.g \(1\) \(15.571\) \(\Q\) None \(-1\) \(1\) \(0\) \(-4\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-4q^{7}-q^{8}+\cdots\)
1950.2.a.h \(1\) \(15.571\) \(\Q\) None \(-1\) \(1\) \(0\) \(-2\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots\)
1950.2.a.i \(1\) \(15.571\) \(\Q\) None \(-1\) \(1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
1950.2.a.j \(1\) \(15.571\) \(\Q\) None \(-1\) \(1\) \(0\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
1950.2.a.k \(1\) \(15.571\) \(\Q\) None \(-1\) \(1\) \(0\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
1950.2.a.l \(1\) \(15.571\) \(\Q\) None \(-1\) \(1\) \(0\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
1950.2.a.m \(1\) \(15.571\) \(\Q\) None \(-1\) \(1\) \(0\) \(1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
1950.2.a.n \(1\) \(15.571\) \(\Q\) None \(1\) \(-1\) \(0\) \(-4\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\)
1950.2.a.o \(1\) \(15.571\) \(\Q\) None \(1\) \(-1\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
1950.2.a.p \(1\) \(15.571\) \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
1950.2.a.q \(1\) \(15.571\) \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
1950.2.a.r \(1\) \(15.571\) \(\Q\) None \(1\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
1950.2.a.s \(1\) \(15.571\) \(\Q\) None \(1\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
1950.2.a.t \(1\) \(15.571\) \(\Q\) None \(1\) \(-1\) \(0\) \(4\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+4q^{7}+q^{8}+\cdots\)
1950.2.a.u \(1\) \(15.571\) \(\Q\) None \(1\) \(-1\) \(0\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+4q^{7}+q^{8}+\cdots\)
1950.2.a.v \(1\) \(15.571\) \(\Q\) None \(1\) \(1\) \(0\) \(-4\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots\)
1950.2.a.w \(1\) \(15.571\) \(\Q\) None \(1\) \(1\) \(0\) \(-4\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots\)
1950.2.a.x \(1\) \(15.571\) \(\Q\) None \(1\) \(1\) \(0\) \(-4\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots\)
1950.2.a.y \(1\) \(15.571\) \(\Q\) None \(1\) \(1\) \(0\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
1950.2.a.z \(1\) \(15.571\) \(\Q\) None \(1\) \(1\) \(0\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
1950.2.a.ba \(1\) \(15.571\) \(\Q\) None \(1\) \(1\) \(0\) \(2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
1950.2.a.bb \(1\) \(15.571\) \(\Q\) None \(1\) \(1\) \(0\) \(3\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots\)
1950.2.a.bc \(2\) \(15.571\) \(\Q(\sqrt{41}) \) None \(-2\) \(-2\) \(0\) \(-3\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+(-1-\beta )q^{7}+\cdots\)
1950.2.a.bd \(2\) \(15.571\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(0\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+\beta q^{7}-q^{8}+\cdots\)
1950.2.a.be \(2\) \(15.571\) \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(0\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+(1+\beta )q^{7}+\cdots\)
1950.2.a.bf \(2\) \(15.571\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+(-1-\beta )q^{7}+\cdots\)
1950.2.a.bg \(2\) \(15.571\) \(\Q(\sqrt{41}) \) None \(2\) \(2\) \(0\) \(3\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+(1+\beta )q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1950))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1950)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(325))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(390))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(650))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(975))\)\(^{\oplus 2}\)