Properties

Label 1950.2.b
Level $1950$
Weight $2$
Character orbit 1950.b
Rep. character $\chi_{1950}(1351,\cdot)$
Character field $\Q$
Dimension $42$
Newform subspaces $13$
Sturm bound $840$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(840\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1950, [\chi])\).

Total New Old
Modular forms 444 42 402
Cusp forms 396 42 354
Eisenstein series 48 0 48

Trace form

\( 42q + 2q^{3} - 42q^{4} + 42q^{9} + O(q^{10}) \) \( 42q + 2q^{3} - 42q^{4} + 42q^{9} - 2q^{12} + 2q^{13} - 12q^{14} + 42q^{16} - 4q^{17} - 8q^{23} + 8q^{26} + 2q^{27} - 28q^{29} - 42q^{36} + 12q^{38} - 18q^{39} + 4q^{42} - 24q^{43} + 2q^{48} - 58q^{49} - 12q^{51} - 2q^{52} + 20q^{53} + 12q^{56} + 60q^{61} + 28q^{62} - 42q^{64} + 4q^{68} - 8q^{69} + 56q^{74} + 64q^{77} - 12q^{78} + 24q^{79} + 42q^{81} + 12q^{82} + 12q^{87} - 24q^{91} + 8q^{92} - 40q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1950, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1950.2.b.a \(2\) \(15.571\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-iq^{2}-q^{3}-q^{4}+iq^{6}+2iq^{7}+\cdots\)
1950.2.b.b \(2\) \(15.571\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+iq^{2}-q^{3}-q^{4}-iq^{6}+3iq^{7}+\cdots\)
1950.2.b.c \(2\) \(15.571\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-iq^{2}-q^{3}-q^{4}+iq^{6}+2iq^{7}+\cdots\)
1950.2.b.d \(2\) \(15.571\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q+iq^{2}+q^{3}-q^{4}+iq^{6}+3iq^{7}+\cdots\)
1950.2.b.e \(2\) \(15.571\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q-iq^{2}+q^{3}-q^{4}-iq^{6}+iq^{8}+q^{9}+\cdots\)
1950.2.b.f \(2\) \(15.571\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q-iq^{2}+q^{3}-q^{4}-iq^{6}+2iq^{7}+\cdots\)
1950.2.b.g \(2\) \(15.571\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q+iq^{2}+q^{3}-q^{4}+iq^{6}-iq^{8}+q^{9}+\cdots\)
1950.2.b.h \(4\) \(15.571\) \(\Q(i, \sqrt{17})\) None \(0\) \(-4\) \(0\) \(0\) \(q-\beta _{1}q^{2}-q^{3}-q^{4}+\beta _{1}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1950.2.b.i \(4\) \(15.571\) \(\Q(i, \sqrt{17})\) None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{2}q^{2}-q^{3}-q^{4}-\beta _{2}q^{6}+(\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots\)
1950.2.b.j \(4\) \(15.571\) \(\Q(i, \sqrt{17})\) None \(0\) \(4\) \(0\) \(0\) \(q+\beta _{2}q^{2}+q^{3}-q^{4}+\beta _{2}q^{6}+(\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots\)
1950.2.b.k \(4\) \(15.571\) \(\Q(i, \sqrt{13})\) None \(0\) \(4\) \(0\) \(0\) \(q+\beta _{1}q^{2}+q^{3}-q^{4}+\beta _{1}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1950.2.b.l \(6\) \(15.571\) 6.0.350464.1 None \(0\) \(-6\) \(0\) \(0\) \(q+\beta _{4}q^{2}-q^{3}-q^{4}-\beta _{4}q^{6}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
1950.2.b.m \(6\) \(15.571\) 6.0.350464.1 None \(0\) \(6\) \(0\) \(0\) \(q+\beta _{4}q^{2}+q^{3}-q^{4}+\beta _{4}q^{6}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1950, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 2}\)