Properties

Label 1950.2.y
Level $1950$
Weight $2$
Character orbit 1950.y
Rep. character $\chi_{1950}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $88$
Newform subspaces $14$
Sturm bound $840$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.y (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 14 \)
Sturm bound: \(840\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 888 88 800
Cusp forms 792 88 704
Eisenstein series 96 0 96

Trace form

\( 88q - 44q^{4} + 44q^{9} + O(q^{10}) \) \( 88q - 44q^{4} + 44q^{9} - 24q^{11} - 16q^{14} - 44q^{16} - 36q^{19} - 24q^{26} - 8q^{29} + 44q^{36} - 12q^{39} + 96q^{41} + 24q^{46} - 64q^{49} - 48q^{51} + 8q^{56} + 72q^{59} - 24q^{61} + 88q^{64} + 16q^{66} - 40q^{69} + 48q^{71} + 36q^{76} - 8q^{79} - 44q^{81} + 12q^{84} - 72q^{89} + 12q^{91} + 16q^{94} + O(q^{100}) \)

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.y.a \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(-6\) \(q+(-1+\zeta_{12}^{2})q^{2}+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
1950.2.y.b \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(-2\) \(q+(-1+\zeta_{12}^{2})q^{2}+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
1950.2.y.c \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(4\) \(q-\zeta_{12}^{2}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1950.2.y.d \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(6\) \(q-\zeta_{12}^{2}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1950.2.y.e \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(0\) \(-6\) \(q+(1-\zeta_{12}^{2})q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
1950.2.y.f \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(0\) \(-4\) \(q+\zeta_{12}^{2}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1950.2.y.g \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(0\) \(2\) \(q+(1-\zeta_{12}^{2})q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
1950.2.y.h \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(0\) \(6\) \(q+\zeta_{12}^{2}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1950.2.y.i \(8\) \(15.571\) \(\Q(\zeta_{24})\) None \(-4\) \(0\) \(0\) \(-4\) \(q+(-1+\zeta_{24}^{4})q^{2}-\zeta_{24}^{2}q^{3}-\zeta_{24}^{4}q^{4}+\cdots\)
1950.2.y.j \(8\) \(15.571\) 8.0.\(\cdots\).1 None \(-4\) \(0\) \(0\) \(2\) \(q+(-1+\beta _{6})q^{2}+(\beta _{2}+\beta _{5})q^{3}-\beta _{6}q^{4}+\cdots\)
1950.2.y.k \(8\) \(15.571\) 8.0.\(\cdots\).1 None \(4\) \(0\) \(0\) \(-2\) \(q+(1-\beta _{6})q^{2}+(-\beta _{2}-\beta _{5})q^{3}-\beta _{6}q^{4}+\cdots\)
1950.2.y.l \(8\) \(15.571\) \(\Q(\zeta_{24})\) None \(4\) \(0\) \(0\) \(4\) \(q+\zeta_{24}^{4}q^{2}+(\zeta_{24}^{2}-\zeta_{24}^{6})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1950.2.y.m \(12\) \(15.571\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-6\) \(0\) \(0\) \(4\) \(q+(-1+\beta _{4})q^{2}-\beta _{9}q^{3}-\beta _{4}q^{4}+\beta _{8}q^{6}+\cdots\)
1950.2.y.n \(12\) \(15.571\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(0\) \(0\) \(-4\) \(q+(1-\beta _{4})q^{2}+\beta _{9}q^{3}-\beta _{4}q^{4}+\beta _{8}q^{6}+\cdots\)

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

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