Properties

Label 1001.2.i
Level $1001$
Weight $2$
Character orbit 1001.i
Rep. character $\chi_{1001}(144,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $160$
Newform subspaces $5$
Sturm bound $224$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1001 = 7 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1001.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 5 \)
Sturm bound: \(224\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1001, [\chi])\).

Total New Old
Modular forms 232 160 72
Cusp forms 216 160 56
Eisenstein series 16 0 16

Trace form

\( 160 q - 80 q^{4} + 8 q^{5} + 16 q^{6} + 24 q^{8} - 88 q^{9} + O(q^{10}) \) \( 160 q - 80 q^{4} + 8 q^{5} + 16 q^{6} + 24 q^{8} - 88 q^{9} - 12 q^{10} - 20 q^{12} + 16 q^{14} + 24 q^{15} - 80 q^{16} - 12 q^{17} - 20 q^{18} - 96 q^{20} + 20 q^{21} + 4 q^{23} + 16 q^{24} - 76 q^{25} + 12 q^{26} - 24 q^{27} - 52 q^{28} + 56 q^{29} - 12 q^{30} + 16 q^{31} - 4 q^{32} + 8 q^{33} + 48 q^{34} + 36 q^{35} + 148 q^{36} - 8 q^{37} - 38 q^{38} + 40 q^{40} - 16 q^{41} - 10 q^{42} + 24 q^{43} - 12 q^{45} - 24 q^{46} + 12 q^{47} + 104 q^{48} + 20 q^{49} - 24 q^{50} - 36 q^{51} + 16 q^{53} - 28 q^{54} - 78 q^{56} - 8 q^{57} - 68 q^{58} + 32 q^{59} - 8 q^{60} - 24 q^{61} + 80 q^{62} - 32 q^{63} + 184 q^{64} + 4 q^{65} - 10 q^{66} - 28 q^{67} - 12 q^{68} - 64 q^{69} - 144 q^{70} - 24 q^{71} - 60 q^{72} + 16 q^{74} - 24 q^{75} + 176 q^{76} + 4 q^{77} + 20 q^{78} + 20 q^{79} + 92 q^{80} - 144 q^{81} + 136 q^{82} + 16 q^{83} + 84 q^{84} + 16 q^{85} + 20 q^{86} - 12 q^{87} - 12 q^{89} + 240 q^{90} - 12 q^{92} - 32 q^{93} + 48 q^{94} - 36 q^{95} - 44 q^{96} - 16 q^{97} - 40 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1001, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1001.2.i.a 1001.i 7.c $8$ $7.993$ 8.0.447703281.1 None \(-2\) \(-1\) \(1\) \(-16\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{3}q^{2}+(-\beta _{5}+\beta _{6})q^{3}+(-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
1001.2.i.b 1001.i 7.c $22$ $7.993$ None \(2\) \(-1\) \(0\) \(15\) $\mathrm{SU}(2)[C_{3}]$
1001.2.i.c 1001.i 7.c $30$ $7.993$ None \(6\) \(2\) \(3\) \(1\) $\mathrm{SU}(2)[C_{3}]$
1001.2.i.d 1001.i 7.c $50$ $7.993$ None \(-6\) \(2\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$
1001.2.i.e 1001.i 7.c $50$ $7.993$ None \(0\) \(-2\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1001, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1001, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)