Properties

Label 1650.2.a
Level $1650$
Weight $2$
Character orbit 1650.a
Rep. character $\chi_{1650}(1,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $26$
Sturm bound $720$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1650.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 26 \)
Sturm bound: \(720\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1650))\).

Total New Old
Modular forms 384 32 352
Cusp forms 337 32 305
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.

\(2\)\(3\)\(5\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(4\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(4\)
Plus space\(+\)\(10\)
Minus space\(-\)\(22\)

Trace form

\( 32q - 2q^{2} + 2q^{3} + 32q^{4} + 4q^{7} - 2q^{8} + 32q^{9} + O(q^{10}) \) \( 32q - 2q^{2} + 2q^{3} + 32q^{4} + 4q^{7} - 2q^{8} + 32q^{9} + 2q^{12} + 32q^{16} + 4q^{17} - 2q^{18} + 28q^{19} + 20q^{21} + 2q^{22} - 4q^{23} + 32q^{26} + 2q^{27} + 4q^{28} + 4q^{29} + 8q^{31} - 2q^{32} + 2q^{33} + 24q^{34} + 32q^{36} + 24q^{37} - 4q^{38} + 28q^{39} + 28q^{41} + 8q^{42} - 4q^{43} + 16q^{46} + 28q^{47} + 2q^{48} + 48q^{49} + 8q^{51} - 12q^{53} + 12q^{57} - 24q^{59} + 40q^{61} + 16q^{62} + 4q^{63} + 32q^{64} - 4q^{66} + 40q^{67} + 4q^{68} + 4q^{69} - 28q^{71} - 2q^{72} - 8q^{73} + 4q^{74} + 28q^{76} + 8q^{77} - 4q^{78} - 20q^{79} + 32q^{81} + 8q^{82} + 20q^{84} + 12q^{86} - 8q^{87} + 2q^{88} - 24q^{89} - 8q^{91} - 4q^{92} + 8q^{94} - 8q^{97} - 2q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1650))\) 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 11
1650.2.a.a \(1\) \(13.175\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-3\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-3q^{7}-q^{8}+\cdots\)
1650.2.a.b \(1\) \(13.175\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
1650.2.a.c \(1\) \(13.175\) \(\Q\) None \(-1\) \(-1\) \(0\) \(2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
1650.2.a.d \(1\) \(13.175\) \(\Q\) None \(-1\) \(-1\) \(0\) \(2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
1650.2.a.e \(1\) \(13.175\) \(\Q\) None \(-1\) \(1\) \(0\) \(-4\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-4q^{7}-q^{8}+\cdots\)
1650.2.a.f \(1\) \(13.175\) \(\Q\) None \(-1\) \(1\) \(0\) \(-3\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots\)
1650.2.a.g \(1\) \(13.175\) \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
1650.2.a.h \(1\) \(13.175\) \(\Q\) None \(-1\) \(1\) \(0\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
1650.2.a.i \(1\) \(13.175\) \(\Q\) None \(-1\) \(1\) \(0\) \(2\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
1650.2.a.j \(1\) \(13.175\) \(\Q\) None \(-1\) \(1\) \(0\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
1650.2.a.k \(1\) \(13.175\) \(\Q\) None \(-1\) \(1\) \(0\) \(4\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots\)
1650.2.a.l \(1\) \(13.175\) \(\Q\) None \(1\) \(-1\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
1650.2.a.m \(1\) \(13.175\) \(\Q\) None \(1\) \(-1\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
1650.2.a.n \(1\) \(13.175\) \(\Q\) None \(1\) \(-1\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
1650.2.a.o \(1\) \(13.175\) \(\Q\) None \(1\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
1650.2.a.p \(1\) \(13.175\) \(\Q\) None \(1\) \(-1\) \(0\) \(3\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+3q^{7}+q^{8}+\cdots\)
1650.2.a.q \(1\) \(13.175\) \(\Q\) None \(1\) \(1\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
1650.2.a.r \(1\) \(13.175\) \(\Q\) None \(1\) \(1\) \(0\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
1650.2.a.s \(1\) \(13.175\) \(\Q\) None \(1\) \(1\) \(0\) \(3\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots\)
1650.2.a.t \(1\) \(13.175\) \(\Q\) None \(1\) \(1\) \(0\) \(4\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots\)
1650.2.a.u \(2\) \(13.175\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(0\) \(-4\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+(-2+\beta )q^{7}+\cdots\)
1650.2.a.v \(2\) \(13.175\) \(\Q(\sqrt{73}) \) None \(-2\) \(-2\) \(0\) \(1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+\beta q^{7}-q^{8}+\cdots\)
1650.2.a.w \(2\) \(13.175\) \(\Q(\sqrt{10}) \) None \(-2\) \(2\) \(0\) \(4\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+(2+\beta )q^{7}+\cdots\)
1650.2.a.x \(2\) \(13.175\) \(\Q(\sqrt{10}) \) None \(2\) \(-2\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+(-2+\beta )q^{7}+\cdots\)
1650.2.a.y \(2\) \(13.175\) \(\Q(\sqrt{73}) \) None \(2\) \(2\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-\beta q^{7}+q^{8}+\cdots\)
1650.2.a.z \(2\) \(13.175\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+(2+\beta )q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1650))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1650)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(550))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(825))\)\(^{\oplus 2}\)