Properties

Label 950.2.b
Level $950$
Weight $2$
Character orbit 950.b
Rep. character $\chi_{950}(799,\cdot)$
Character field $\Q$
Dimension $26$
Newform subspaces $8$
Sturm bound $300$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(300\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(950, [\chi])\).

Total New Old
Modular forms 162 26 136
Cusp forms 138 26 112
Eisenstein series 24 0 24

Trace form

\( 26 q - 26 q^{4} + 4 q^{6} - 38 q^{9} + O(q^{10}) \) \( 26 q - 26 q^{4} + 4 q^{6} - 38 q^{9} + 8 q^{11} - 8 q^{14} + 26 q^{16} + 2 q^{19} + 32 q^{21} - 4 q^{24} - 24 q^{26} - 28 q^{29} + 4 q^{34} + 38 q^{36} - 8 q^{39} - 12 q^{41} - 8 q^{44} + 40 q^{46} - 62 q^{49} + 40 q^{51} - 16 q^{54} + 8 q^{56} - 24 q^{59} + 36 q^{61} - 26 q^{64} + 56 q^{69} + 8 q^{71} + 48 q^{74} - 2 q^{76} - 48 q^{79} + 42 q^{81} - 32 q^{84} + 52 q^{89} - 24 q^{91} - 56 q^{94} + 4 q^{96} + 32 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(950, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
950.2.b.a 950.b 5.b $2$ $7.586$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+3iq^{3}-q^{4}-3q^{6}-5iq^{7}+\cdots\)
950.2.b.b 950.b 5.b $2$ $7.586$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
950.2.b.c 950.b 5.b $2$ $7.586$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+3iq^{7}+\cdots\)
950.2.b.d 950.b 5.b $2$ $7.586$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+q^{6}-iq^{7}+iq^{8}+\cdots\)
950.2.b.e 950.b 5.b $2$ $7.586$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{7}+iq^{8}+\cdots\)
950.2.b.f 950.b 5.b $4$ $7.586$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(1-\beta _{3})q^{6}+\cdots\)
950.2.b.g 950.b 5.b $6$ $7.586$ 6.0.4227136.2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}+(\beta _{1}-\beta _{3}-\beta _{4})q^{3}-q^{4}+\cdots\)
950.2.b.h 950.b 5.b $6$ $7.586$ 6.0.63107136.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+(\beta _{1}-\beta _{3})q^{3}-q^{4}+(1-\beta _{2}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(950, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)