Properties

Label 1005.2.c
Level $1005$
Weight $2$
Character orbit 1005.c
Rep. character $\chi_{1005}(604,\cdot)$
Character field $\Q$
Dimension $68$
Newform subspaces $4$
Sturm bound $272$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1005 = 3 \cdot 5 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1005.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(272\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1005, [\chi])\).

Total New Old
Modular forms 140 68 72
Cusp forms 132 68 64
Eisenstein series 8 0 8

Trace form

\( 68 q - 68 q^{4} - 68 q^{9} + O(q^{10}) \) \( 68 q - 68 q^{4} - 68 q^{9} - 12 q^{10} + 24 q^{14} - 4 q^{15} + 68 q^{16} + 8 q^{20} + 8 q^{21} - 4 q^{25} - 40 q^{26} - 8 q^{29} - 16 q^{30} + 40 q^{34} + 20 q^{35} + 68 q^{36} - 16 q^{39} + 28 q^{40} - 16 q^{41} - 48 q^{44} + 40 q^{46} - 92 q^{49} + 8 q^{50} - 8 q^{51} + 48 q^{55} + 16 q^{59} - 8 q^{60} - 16 q^{61} - 44 q^{64} + 52 q^{65} - 8 q^{66} + 16 q^{69} - 64 q^{70} - 32 q^{71} - 8 q^{74} + 24 q^{75} - 32 q^{76} - 32 q^{79} - 32 q^{80} + 68 q^{81} - 8 q^{85} - 16 q^{86} - 16 q^{89} + 12 q^{90} + 8 q^{91} + 8 q^{94} - 16 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1005, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1005.2.c.a 1005.c 5.b $2$ $8.025$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}+q^{4}+(2+i)q^{5}-q^{6}+\cdots\)
1005.2.c.b 1005.c 5.b $4$ $8.025$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{3})q^{2}+\beta _{2}q^{3}-4q^{4}+(-1+\cdots)q^{5}+\cdots\)
1005.2.c.c 1005.c 5.b $28$ $8.025$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1005.2.c.d 1005.c 5.b $34$ $8.025$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1005, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1005, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 2}\)