Properties

Label 1170.2.i
Level $1170$
Weight $2$
Character orbit 1170.i
Rep. character $\chi_{1170}(451,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $44$
Newform subspaces $17$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 17 \)
Sturm bound: \(504\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\), \(29\)

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

\( 44q - 22q^{4} + 8q^{7} + O(q^{10}) \) \( 44q - 22q^{4} + 8q^{7} + 2q^{10} - 14q^{11} - 4q^{13} - 4q^{14} - 22q^{16} - 8q^{17} - 6q^{19} + 8q^{22} - 8q^{23} + 44q^{25} - 8q^{26} + 8q^{28} + 20q^{29} - 8q^{31} + 16q^{34} - 6q^{35} + 4q^{37} + 24q^{38} - 4q^{40} + 20q^{41} + 16q^{43} + 28q^{44} + 16q^{46} + 16q^{47} - 12q^{49} + 8q^{52} - 16q^{53} - 4q^{55} + 2q^{56} - 20q^{58} + 16q^{59} - 24q^{61} + 44q^{64} - 10q^{65} - 16q^{67} - 8q^{68} + 56q^{73} + 2q^{74} - 6q^{76} + 24q^{77} + 104q^{79} - 48q^{83} - 12q^{85} - 56q^{86} + 8q^{88} - 46q^{89} + 106q^{91} + 16q^{92} - 2q^{94} - 44q^{97} - 32q^{98} + O(q^{100}) \)

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.i.a \(2\) \(9.342\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(2\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}+2\zeta_{6}q^{7}+\cdots\)
1170.2.i.b \(2\) \(9.342\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(4\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}+4\zeta_{6}q^{7}+\cdots\)
1170.2.i.c \(2\) \(9.342\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(-3\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}-3\zeta_{6}q^{7}+\cdots\)
1170.2.i.d \(2\) \(9.342\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(-2\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}-2\zeta_{6}q^{7}+\cdots\)
1170.2.i.e \(2\) \(9.342\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(0\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+q^{8}+\cdots\)
1170.2.i.f \(2\) \(9.342\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(1\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+\zeta_{6}q^{7}+\cdots\)
1170.2.i.g \(2\) \(9.342\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(5\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+5\zeta_{6}q^{7}+\cdots\)
1170.2.i.h \(2\) \(9.342\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-2\) \(0\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
1170.2.i.i \(2\) \(9.342\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-2\) \(3\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}+3\zeta_{6}q^{7}+\cdots\)
1170.2.i.j \(2\) \(9.342\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-2\) \(3\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}+3\zeta_{6}q^{7}+\cdots\)
1170.2.i.k \(2\) \(9.342\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(2\) \(-2\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}-2\zeta_{6}q^{7}+\cdots\)
1170.2.i.l \(2\) \(9.342\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(2\) \(4\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+4\zeta_{6}q^{7}+\cdots\)
1170.2.i.m \(4\) \(9.342\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(-4\) \(-4\) \(q+(-1+\zeta_{12})q^{2}-\zeta_{12}q^{4}-q^{5}+(-2\zeta_{12}+\cdots)q^{7}+\cdots\)
1170.2.i.n \(4\) \(9.342\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(-4\) \(2\) \(q+(-1+\zeta_{12})q^{2}-\zeta_{12}q^{4}-q^{5}+(\zeta_{12}+\cdots)q^{7}+\cdots\)
1170.2.i.o \(4\) \(9.342\) \(\Q(\sqrt{-3}, \sqrt{17})\) None \(2\) \(0\) \(-4\) \(-3\) \(q+(1-\beta _{2})q^{2}-\beta _{2}q^{4}-q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1170.2.i.p \(4\) \(9.342\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(4\) \(-4\) \(q+(1-\zeta_{12})q^{2}-\zeta_{12}q^{4}+q^{5}+(-2\zeta_{12}+\cdots)q^{7}+\cdots\)
1170.2.i.q \(4\) \(9.342\) \(\Q(\sqrt{-3}, \sqrt{10})\) None \(2\) \(0\) \(4\) \(2\) \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+q^{5}-\beta _{2}q^{7}+\cdots\)

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

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