Properties

Label 950.2.l
Level $950$
Weight $2$
Character orbit 950.l
Rep. character $\chi_{950}(101,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $186$
Newform subspaces $13$
Sturm bound $300$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.l (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 13 \)
Sturm bound: \(300\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 972 186 786
Cusp forms 828 186 642
Eisenstein series 144 0 144

Trace form

\( 186q - 3q^{3} - 3q^{6} + 6q^{7} - 3q^{8} - 3q^{9} + O(q^{10}) \) \( 186q - 3q^{3} - 3q^{6} + 6q^{7} - 3q^{8} - 3q^{9} + 6q^{11} + 12q^{13} - 12q^{14} + 24q^{17} + 42q^{18} + 42q^{19} + 48q^{21} + 24q^{22} + 36q^{23} - 3q^{24} - 6q^{26} + 3q^{27} - 6q^{28} + 6q^{29} + 6q^{31} - 45q^{33} - 12q^{34} - 3q^{36} - 12q^{37} - 9q^{38} + 84q^{39} + 15q^{41} - 12q^{42} - 30q^{43} + 12q^{44} + 54q^{47} + 6q^{48} - 45q^{49} - 69q^{51} - 6q^{52} + 60q^{53} + 45q^{54} - 36q^{56} + 108q^{57} + 24q^{58} + 51q^{59} - 102q^{61} + 42q^{62} + 48q^{63} - 93q^{64} - 63q^{66} - 9q^{67} + 9q^{68} + 42q^{69} - 18q^{71} + 6q^{72} + 6q^{73} + 18q^{74} + 6q^{76} - 60q^{77} - 18q^{78} + 6q^{79} + 15q^{81} - 45q^{82} - 30q^{83} - 6q^{84} - 36q^{86} - 102q^{87} - 6q^{88} - 96q^{89} - 48q^{91} - 18q^{92} - 78q^{93} + 12q^{94} - 21q^{97} - 24q^{98} + 21q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
950.2.l.a \(6\) \(7.586\) \(\Q(\zeta_{18})\) None \(0\) \(-6\) \(0\) \(0\) \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+(-1-\zeta_{18}^{2})q^{3}+\cdots\)
950.2.l.b \(6\) \(7.586\) \(\Q(\zeta_{18})\) None \(0\) \(-3\) \(0\) \(-3\) \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(-1-\zeta_{18}+\cdots)q^{3}+\cdots\)
950.2.l.c \(6\) \(7.586\) \(\Q(\zeta_{18})\) None \(0\) \(-3\) \(0\) \(0\) \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(-\zeta_{18}^{2}-\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
950.2.l.d \(6\) \(7.586\) \(\Q(\zeta_{18})\) None \(0\) \(3\) \(0\) \(6\) \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
950.2.l.e \(6\) \(7.586\) \(\Q(\zeta_{18})\) None \(0\) \(3\) \(0\) \(3\) \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+(1+\zeta_{18}-\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
950.2.l.f \(6\) \(7.586\) \(\Q(\zeta_{18})\) None \(0\) \(6\) \(0\) \(0\) \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(1+\zeta_{18}^{2})q^{3}+\cdots\)
950.2.l.g \(12\) \(7.586\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-3\) \(0\) \(6\) \(q+\beta _{8}q^{2}+\beta _{4}q^{3}+\beta _{10}q^{4}+(\beta _{6}-\beta _{8}+\cdots)q^{6}+\cdots\)
950.2.l.h \(12\) \(7.586\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(-6\) \(q+\beta _{2}q^{2}+\beta _{3}q^{3}-\beta _{7}q^{4}+(\beta _{1}-\beta _{4}+\cdots)q^{6}+\cdots\)
950.2.l.i \(18\) \(7.586\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{9}q^{2}+\beta _{7}q^{3}-\beta _{11}q^{4}+\beta _{5}q^{6}+\cdots\)
950.2.l.j \(24\) \(7.586\) None \(0\) \(0\) \(0\) \(-3\)
950.2.l.k \(24\) \(7.586\) None \(0\) \(0\) \(0\) \(3\)
950.2.l.l \(30\) \(7.586\) None \(0\) \(0\) \(0\) \(-12\)
950.2.l.m \(30\) \(7.586\) None \(0\) \(0\) \(0\) \(12\)

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

\( S_{2}^{\mathrm{old}}(950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)