Properties

Label 1170.2.bs
Level $1170$
Weight $2$
Character orbit 1170.bs
Rep. character $\chi_{1170}(361,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $44$
Newform subspaces $8$
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.bs (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 8 \)
Sturm bound: \(504\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

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

Total New Old
Modular forms 536 44 492
Cusp forms 472 44 428
Eisenstein series 64 0 64

Trace form

\( 44q + 22q^{4} + O(q^{10}) \) \( 44q + 22q^{4} + 2q^{10} - 6q^{11} + 12q^{13} - 12q^{14} - 22q^{16} - 16q^{17} - 18q^{19} - 44q^{25} + 16q^{26} - 4q^{29} + 2q^{35} + 36q^{37} + 24q^{38} + 4q^{40} + 24q^{41} - 12q^{46} + 28q^{49} - 32q^{53} - 12q^{55} - 6q^{56} + 12q^{58} - 36q^{59} + 8q^{61} - 32q^{62} - 44q^{64} + 14q^{65} + 72q^{67} + 16q^{68} + 72q^{71} - 22q^{74} - 18q^{76} + 8q^{77} + 8q^{79} + 16q^{82} - 36q^{85} + 30q^{89} + 38q^{91} - 10q^{94} - 16q^{95} - 12q^{97} + O(q^{100}) \)

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.bs.a \(4\) \(9.342\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-6\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}+(-2+\cdots)q^{7}+\cdots\)
1170.2.bs.b \(4\) \(9.342\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)
1170.2.bs.c \(4\) \(9.342\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots\)
1170.2.bs.d \(4\) \(9.342\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots\)
1170.2.bs.e \(4\) \(9.342\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots\)
1170.2.bs.f \(8\) \(9.342\) 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{2}-\beta _{5})q^{2}+\beta _{6}q^{4}-\beta _{2}q^{5}+\cdots\)
1170.2.bs.g \(8\) \(9.342\) 8.0.22581504.2 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1-\beta _{4})q^{4}+(-\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots\)
1170.2.bs.h \(8\) \(9.342\) 8.0.1731891456.1 None \(0\) \(0\) \(0\) \(6\) \(q-\beta _{3}q^{2}+(1-\beta _{2})q^{4}-\beta _{5}q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1170, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)