Properties

Label 1170.2.e
Level $1170$
Weight $2$
Character orbit 1170.e
Rep. character $\chi_{1170}(469,\cdot)$
Character field $\Q$
Dimension $30$
Newform subspaces $8$
Sturm bound $504$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(504\)
Trace bound: \(11\)
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 268 30 238
Cusp forms 236 30 206
Eisenstein series 32 0 32

Trace form

\( 30 q - 30 q^{4} - 8 q^{5} + O(q^{10}) \) \( 30 q - 30 q^{4} - 8 q^{5} + 4 q^{10} + 4 q^{11} - 4 q^{14} + 30 q^{16} - 4 q^{19} + 8 q^{20} - 8 q^{25} - 6 q^{26} - 4 q^{29} + 8 q^{31} - 8 q^{34} + 30 q^{35} - 4 q^{40} - 20 q^{41} - 4 q^{44} - 20 q^{46} - 18 q^{49} + 16 q^{50} + 16 q^{55} + 4 q^{56} - 12 q^{59} - 28 q^{61} - 30 q^{64} + 4 q^{65} + 28 q^{70} + 16 q^{71} + 4 q^{76} + 8 q^{79} - 8 q^{80} + 12 q^{85} - 8 q^{86} - 36 q^{89} + 12 q^{91} + 20 q^{94} - 20 q^{95} + O(q^{100}) \)

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.e.a \(2\) \(9.342\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-iq^{2}-q^{4}+(-2-i)q^{5}+2iq^{7}+\cdots\)
1170.2.e.b \(2\) \(9.342\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-iq^{2}-q^{4}+(-2+i)q^{5}+4iq^{7}+\cdots\)
1170.2.e.c \(2\) \(9.342\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{2}-q^{4}+(-2-i)q^{5}+4iq^{7}+\cdots\)
1170.2.e.d \(2\) \(9.342\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q-iq^{2}-q^{4}+(2+i)q^{5}+iq^{8}+(1+\cdots)q^{10}+\cdots\)
1170.2.e.e \(4\) \(9.342\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1170.2.e.f \(6\) \(9.342\) 6.0.3534400.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}-q^{4}+(-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
1170.2.e.g \(6\) \(9.342\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}-q^{4}+(-\beta _{2}+\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1170.2.e.h \(6\) \(9.342\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}-q^{4}+(\beta _{2}-\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1170, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)