Properties

Label 1050.2.bc
Level $1050$
Weight $2$
Character orbit 1050.bc
Rep. character $\chi_{1050}(157,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $96$
Newform subspaces $8$
Sturm bound $480$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.bc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 8 \)
Sturm bound: \(480\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\)

Dimensions

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

Total New Old
Modular forms 1056 96 960
Cusp forms 864 96 768
Eisenstein series 192 0 192

Trace form

\( 96q + 12q^{7} + O(q^{10}) \) \( 96q + 12q^{7} - 16q^{11} + 48q^{16} + 8q^{21} - 8q^{22} + 8q^{23} + 48q^{26} + 12q^{28} + 96q^{31} - 12q^{33} - 96q^{36} + 16q^{37} + 48q^{38} - 4q^{42} + 48q^{43} + 16q^{46} + 24q^{47} - 32q^{51} - 16q^{53} - 32q^{56} + 16q^{57} - 36q^{58} + 24q^{61} + 48q^{67} + 128q^{71} + 24q^{73} + 32q^{78} + 48q^{81} - 48q^{82} + 32q^{86} - 60q^{87} - 4q^{88} + 8q^{91} - 16q^{92} - 8q^{93} - 16q^{98} + O(q^{100}) \)

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.bc.a \(8\) \(8.384\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}+(-\zeta_{24}^{3}+\zeta_{24}^{7})q^{3}+\cdots\)
1050.2.bc.b \(8\) \(8.384\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}^{3}-\zeta_{24}^{7})q^{2}+\zeta_{24}^{7}q^{3}+(\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
1050.2.bc.c \(8\) \(8.384\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}+(\zeta_{24}^{3}-\zeta_{24}^{7})q^{3}-\zeta_{24}^{2}q^{4}+\cdots\)
1050.2.bc.d \(8\) \(8.384\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}q^{2}-\zeta_{24}^{5}q^{3}+\zeta_{24}^{2}q^{4}+\zeta_{24}^{6}q^{6}+\cdots\)
1050.2.bc.e \(16\) \(8.384\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}-\beta _{11}q^{3}+(\beta _{8}-\beta _{9})q^{4}-\beta _{9}q^{6}+\cdots\)
1050.2.bc.f \(16\) \(8.384\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{11}q^{2}+\beta _{2}q^{3}-\beta _{8}q^{4}+\beta _{9}q^{6}+\cdots\)
1050.2.bc.g \(16\) \(8.384\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{6}q^{2}-\beta _{12}q^{3}+(-\beta _{5}+\beta _{13})q^{4}+\cdots\)
1050.2.bc.h \(16\) \(8.384\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(8\) \(q+\beta _{15}q^{2}+\beta _{2}q^{3}+(\beta _{5}-\beta _{13})q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)