Properties

Label 1050.2.d
Level $1050$
Weight $2$
Character orbit 1050.d
Rep. character $\chi_{1050}(1049,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $8$
Sturm bound $480$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(480\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(11\), \(13\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1050, [\chi])\).

Total New Old
Modular forms 264 48 216
Cusp forms 216 48 168
Eisenstein series 48 0 48

Trace form

\( 48q + 48q^{4} + O(q^{10}) \) \( 48q + 48q^{4} + 48q^{16} + 20q^{21} + 48q^{39} + 56q^{46} - 16q^{49} + 40q^{51} + 48q^{64} - 32q^{79} - 88q^{81} + 20q^{84} - 56q^{91} - 96q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1050, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1050.2.d.a \(4\) \(8.384\) \(\Q(i, \sqrt{5})\) None \(-4\) \(-2\) \(0\) \(6\) \(q-q^{2}+(-\beta _{2}-\beta _{3})q^{3}+q^{4}+(\beta _{2}+\beta _{3})q^{6}+\cdots\)
1050.2.d.b \(4\) \(8.384\) \(\Q(i, \sqrt{6})\) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta _{3}q^{3}+q^{4}+\beta _{3}q^{6}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1050.2.d.c \(4\) \(8.384\) \(\Q(i, \sqrt{5})\) None \(-4\) \(2\) \(0\) \(-6\) \(q-q^{2}+(\beta _{2}+\beta _{3})q^{3}+q^{4}+(-\beta _{2}-\beta _{3})q^{6}+\cdots\)
1050.2.d.d \(4\) \(8.384\) \(\Q(i, \sqrt{5})\) None \(4\) \(-2\) \(0\) \(6\) \(q+q^{2}+(-\beta _{2}-\beta _{3})q^{3}+q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
1050.2.d.e \(4\) \(8.384\) \(\Q(i, \sqrt{6})\) None \(4\) \(0\) \(0\) \(0\) \(q+q^{2}+\beta _{3}q^{3}+q^{4}+\beta _{3}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1050.2.d.f \(4\) \(8.384\) \(\Q(i, \sqrt{5})\) None \(4\) \(2\) \(0\) \(-6\) \(q+q^{2}+(\beta _{2}+\beta _{3})q^{3}+q^{4}+(\beta _{2}+\beta _{3})q^{6}+\cdots\)
1050.2.d.g \(12\) \(8.384\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-12\) \(0\) \(0\) \(0\) \(q-q^{2}+\beta _{10}q^{3}+q^{4}-\beta _{10}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1050.2.d.h \(12\) \(8.384\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(12\) \(0\) \(0\) \(0\) \(q+q^{2}-\beta _{10}q^{3}+q^{4}-\beta _{10}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1050, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)