Properties

Label 605.2.b
Level $605$
Weight $2$
Character orbit 605.b
Rep. character $\chi_{605}(364,\cdot)$
Character field $\Q$
Dimension $46$
Newform subspaces $8$
Sturm bound $132$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(132\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(605, [\chi])\).

Total New Old
Modular forms 78 64 14
Cusp forms 54 46 8
Eisenstein series 24 18 6

Trace form

\( 46 q - 34 q^{4} + 2 q^{5} - 8 q^{6} - 26 q^{9} + O(q^{10}) \) \( 46 q - 34 q^{4} + 2 q^{5} - 8 q^{6} - 26 q^{9} + 10 q^{10} - 16 q^{14} + 2 q^{15} + 10 q^{16} + 16 q^{19} + 16 q^{20} - 12 q^{21} - 4 q^{24} + 2 q^{25} + 44 q^{26} + 12 q^{29} + 6 q^{30} - 8 q^{31} - 40 q^{34} - 18 q^{35} + 22 q^{36} - 28 q^{40} - 12 q^{41} - 36 q^{45} + 8 q^{46} + 30 q^{49} + 18 q^{50} + 28 q^{51} - 20 q^{54} + 52 q^{56} - 24 q^{59} - 40 q^{60} - 20 q^{61} + 38 q^{64} - 4 q^{69} - 8 q^{70} + 24 q^{71} - 12 q^{74} + 26 q^{75} - 24 q^{76} + 28 q^{79} - 56 q^{80} - 18 q^{81} - 48 q^{84} - 2 q^{85} - 4 q^{86} - 36 q^{89} + 28 q^{90} - 8 q^{91} + 44 q^{94} - 12 q^{95} - 36 q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(605, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
605.2.b.a 605.b 5.b $2$ $4.831$ \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) \(0\) \(0\) \(3\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-1+2\beta )q^{3}+2q^{4}+(1+\beta )q^{5}+\cdots\)
605.2.b.b 605.b 5.b $4$ $4.831$ 4.0.4400.1 \(\Q(\sqrt{-55}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{2}+(-2-\beta _{3})q^{4}+\beta _{3}q^{5}-\beta _{1}q^{7}+\cdots\)
605.2.b.c 605.b 5.b $4$ $4.831$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\cdots\)
605.2.b.d 605.b 5.b $4$ $4.831$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
605.2.b.e 605.b 5.b $4$ $4.831$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
605.2.b.f 605.b 5.b $8$ $4.831$ 8.0.1480160000.1 None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{6}+\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots\)
605.2.b.g 605.b 5.b $8$ $4.831$ 8.0.1480160000.1 None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{6}-\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots\)
605.2.b.h 605.b 5.b $12$ $4.831$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{9}q^{2}-\beta _{8}q^{3}+(-2-\beta _{6})q^{4}+\beta _{4}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(605, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(605, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)