Properties

Label 950.2.q
Level $950$
Weight $2$
Character orbit 950.q
Rep. character $\chi_{950}(107,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $120$
Newform subspaces $7$
Sturm bound $300$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.q (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 7 \)
Sturm bound: \(300\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

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

Total New Old
Modular forms 648 120 528
Cusp forms 552 120 432
Eisenstein series 96 0 96

Trace form

\( 120q - 8q^{7} + O(q^{10}) \) \( 120q - 8q^{7} + 16q^{11} + 60q^{16} + 16q^{17} - 24q^{21} + 24q^{22} - 4q^{23} + 32q^{26} + 4q^{28} + 12q^{33} - 60q^{36} - 4q^{38} - 24q^{41} - 32q^{42} + 4q^{43} + 36q^{47} - 132q^{51} + 36q^{53} + 36q^{57} - 8q^{61} - 8q^{62} + 8q^{63} + 44q^{66} - 24q^{67} - 32q^{68} - 24q^{73} + 24q^{76} + 64q^{77} + 24q^{78} + 60q^{81} - 8q^{82} - 64q^{83} - 48q^{86} - 152q^{87} - 264q^{91} + 4q^{92} - 28q^{93} + 12q^{97} - 120q^{98} + O(q^{100}) \)

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.q.a \(8\) \(7.586\) \(\Q(\zeta_{24})\) None \(0\) \(-12\) \(0\) \(16\) \(q-\zeta_{24}q^{2}+(-2+\zeta_{24}^{2}+\zeta_{24}^{4}+\zeta_{24}^{6}+\cdots)q^{3}+\cdots\)
950.2.q.b \(8\) \(7.586\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}q^{2}+\zeta_{24}^{7}q^{3}+\zeta_{24}^{2}q^{4}+(-1+\cdots)q^{6}+\cdots\)
950.2.q.c \(8\) \(7.586\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}q^{2}+\zeta_{24}^{7}q^{3}+\zeta_{24}^{2}q^{4}+(1+\cdots)q^{6}+\cdots\)
950.2.q.d \(8\) \(7.586\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}q^{2}+2\zeta_{24}^{7}q^{3}+\zeta_{24}^{2}q^{4}+\cdots\)
950.2.q.e \(24\) \(7.586\) None \(0\) \(0\) \(0\) \(0\)
950.2.q.f \(32\) \(7.586\) None \(0\) \(0\) \(0\) \(0\)
950.2.q.g \(32\) \(7.586\) None \(0\) \(12\) \(0\) \(-24\)

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

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