Properties

Label 1170.2.b
Level $1170$
Weight $2$
Character orbit 1170.b
Rep. character $\chi_{1170}(181,\cdot)$
Character field $\Q$
Dimension $26$
Newform subspaces $7$
Sturm bound $504$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(504\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1170, [\chi])\).

Total New Old
Modular forms 268 26 242
Cusp forms 236 26 210
Eisenstein series 32 0 32

Trace form

\( 26q - 26q^{4} + O(q^{10}) \) \( 26q - 26q^{4} - 2q^{10} - 4q^{13} + 26q^{16} + 4q^{17} - 26q^{25} - 10q^{26} - 20q^{29} - 8q^{35} + 24q^{38} + 2q^{40} - 4q^{43} - 42q^{49} + 4q^{52} + 8q^{53} + 20q^{61} - 4q^{62} - 26q^{64} - 2q^{65} - 4q^{68} - 20q^{74} + 64q^{77} - 16q^{79} - 16q^{82} + 40q^{91} - 8q^{94} - 32q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1170, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1170.2.b.a \(2\) \(9.342\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+iq^{5}-iq^{8}-q^{10}+\cdots\)
1170.2.b.b \(2\) \(9.342\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{5}-iq^{8}+q^{10}+\cdots\)
1170.2.b.c \(2\) \(9.342\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{5}+iq^{8}+q^{10}+\cdots\)
1170.2.b.d \(4\) \(9.342\) \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-q^{4}-\beta _{1}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1170.2.b.e \(4\) \(9.342\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}-q^{4}-\zeta_{12}q^{5}-\zeta_{12}q^{8}+\cdots\)
1170.2.b.f \(4\) \(9.342\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-q^{4}-\beta _{1}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1170.2.b.g \(8\) \(9.342\) 8.0.3057647616.6 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-q^{4}-\beta _{1}q^{5}-\beta _{7}q^{7}+\beta _{1}q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1170, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1170, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)