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Properties

Label 950.2.e
Level $950$
Weight $2$
Character orbit 950.e
Rep. character $\chi_{950}(201,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $66$
Newform subspaces $15$
Sturm bound $300$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 15 \)
Sturm bound: \(300\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

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

Total New Old
Modular forms 324 66 258
Cusp forms 276 66 210
Eisenstein series 48 0 48

Trace form

\( 66 q - q^{2} - q^{3} - 33 q^{4} + q^{6} - 12 q^{7} + 2 q^{8} - 36 q^{9} + O(q^{10}) \) \( 66 q - q^{2} - q^{3} - 33 q^{4} + q^{6} - 12 q^{7} + 2 q^{8} - 36 q^{9} - 2 q^{11} + 2 q^{12} + 10 q^{13} - 2 q^{14} - 33 q^{16} - 2 q^{17} - 12 q^{18} + 25 q^{19} + 26 q^{21} - q^{22} - 8 q^{23} + q^{24} - 12 q^{26} + 14 q^{27} + 6 q^{28} + 6 q^{29} - 16 q^{31} - q^{32} - 9 q^{33} + 2 q^{34} - 36 q^{36} + 8 q^{37} + 12 q^{38} - 52 q^{39} + 25 q^{41} + 14 q^{42} + 12 q^{43} + q^{44} - 24 q^{46} + 22 q^{47} - q^{48} + 42 q^{49} - 16 q^{51} + 10 q^{52} + 2 q^{53} - 29 q^{54} + 4 q^{56} - 16 q^{57} - 4 q^{58} + 35 q^{59} + 10 q^{61} + 8 q^{63} + 66 q^{64} - 9 q^{66} + 19 q^{67} + 4 q^{68} + 8 q^{69} + 2 q^{71} + 6 q^{72} + 27 q^{73} + 4 q^{74} - 17 q^{76} + 52 q^{77} + 2 q^{78} - 69 q^{81} - 9 q^{82} - 10 q^{83} - 52 q^{84} - 16 q^{86} - 28 q^{87} + 2 q^{88} + 34 q^{89} - 32 q^{91} - 8 q^{92} - 40 q^{93} - 52 q^{94} - 2 q^{96} - 27 q^{97} - 17 q^{98} - 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
950.2.e.a 950.e 19.c $2$ $7.586$ \(\Q(\sqrt{-3}) \) None 190.2.e.b \(-1\) \(-1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
950.2.e.b 950.e 19.c $2$ $7.586$ \(\Q(\sqrt{-3}) \) None 950.2.e.b \(-1\) \(-1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
950.2.e.c 950.e 19.c $2$ $7.586$ \(\Q(\sqrt{-3}) \) None 950.2.e.c \(-1\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+4q^{7}+q^{8}+\cdots\)
950.2.e.d 950.e 19.c $2$ $7.586$ \(\Q(\sqrt{-3}) \) None 38.2.c.a \(-1\) \(1\) \(0\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
950.2.e.e 950.e 19.c $2$ $7.586$ \(\Q(\sqrt{-3}) \) None 950.2.e.c \(1\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-4q^{7}-q^{8}+\cdots\)
950.2.e.f 950.e 19.c $2$ $7.586$ \(\Q(\sqrt{-3}) \) None 190.2.e.a \(1\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{7}-q^{8}+3\zeta_{6}q^{9}+\cdots\)
950.2.e.g 950.e 19.c $2$ $7.586$ \(\Q(\sqrt{-3}) \) None 950.2.e.b \(1\) \(1\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
950.2.e.h 950.e 19.c $4$ $7.586$ \(\Q(\sqrt{-3}, \sqrt{17})\) None 190.2.e.c \(-2\) \(-1\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}-\beta _{1}q^{3}+(-1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.e.i 950.e 19.c $4$ $7.586$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None 950.2.e.i \(-2\) \(1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{1})q^{2}+\beta _{3}q^{3}+\beta _{1}q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
950.2.e.j 950.e 19.c $4$ $7.586$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None 950.2.e.i \(2\) \(-1\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1})q^{2}-\beta _{3}q^{3}+\beta _{1}q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
950.2.e.k 950.e 19.c $4$ $7.586$ \(\Q(\sqrt{-3}, \sqrt{7})\) None 38.2.c.b \(2\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.e.l 950.e 19.c $8$ $7.586$ 8.0.\(\cdots\).1 None 950.2.e.l \(-4\) \(1\) \(0\) \(12\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{5}q^{2}+\beta _{1}q^{3}+(-1-\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.e.m 950.e 19.c $8$ $7.586$ 8.0.\(\cdots\).1 None 950.2.e.l \(4\) \(-1\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{5}q^{2}-\beta _{1}q^{3}+(-1-\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.e.n 950.e 19.c $10$ $7.586$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 190.2.i.a \(-5\) \(0\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{5}q^{2}+\beta _{1}q^{3}+(-1-\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.e.o 950.e 19.c $10$ $7.586$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 190.2.i.a \(5\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{5}q^{2}-\beta _{1}q^{3}+(-1-\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(950, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)