Properties

Label 1950.2.z
Level $1950$
Weight $2$
Character orbit 1950.z
Rep. character $\chi_{1950}(1699,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $16$
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.z (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 16 \)
Sturm bound: \(840\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\)

Dimensions

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

Total New Old
Modular forms 888 80 808
Cusp forms 792 80 712
Eisenstein series 96 0 96

Trace form

\( 80q + 40q^{4} + 40q^{9} + O(q^{10}) \) \( 80q + 40q^{4} + 40q^{9} + 8q^{11} + 16q^{14} - 40q^{16} - 20q^{19} + 8q^{21} + 28q^{26} - 4q^{29} - 32q^{31} - 56q^{34} - 40q^{36} + 4q^{39} - 52q^{41} + 16q^{44} - 8q^{46} + 36q^{49} + 16q^{51} + 8q^{56} + 72q^{59} + 20q^{61} - 80q^{64} - 48q^{66} + 8q^{69} + 80q^{71} + 20q^{74} + 20q^{76} + 40q^{79} - 40q^{81} + 4q^{84} + 48q^{86} - 80q^{89} - 36q^{91} - 32q^{94} + 16q^{99} + O(q^{100}) \)

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.z.a \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.b \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.c \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.d \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.e \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.f \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.g \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.h \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.i \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.j \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.k \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.l \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.m \(8\) \(15.571\) 8.0.1731891456.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}+\beta _{7})q^{2}+(-\beta _{3}-\beta _{7})q^{3}-\beta _{2}q^{4}+\cdots\)
1950.2.z.n \(8\) \(15.571\) 8.0.1731891456.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{3}-\beta _{7})q^{2}+(\beta _{3}+\beta _{7})q^{3}-\beta _{2}q^{4}+\cdots\)
1950.2.z.o \(8\) \(15.571\) 8.0.3317760000.2 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{3})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\cdots\)
1950.2.z.p \(8\) \(15.571\) 8.0.3317760000.2 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}+\beta _{2}q^{6}+\cdots\)

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

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