Properties

Label 950.2.u
Level $950$
Weight $2$
Character orbit 950.u
Rep. character $\chi_{950}(99,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $180$
Newform subspaces $8$
Sturm bound $300$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.u (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 8 \)
Sturm bound: \(300\)
Trace bound: \(9\)
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 972 180 792
Cusp forms 828 180 648
Eisenstein series 144 0 144

Trace form

\( 180q + O(q^{10}) \) \( 180q - 12q^{11} + 24q^{14} - 24q^{19} + 24q^{21} - 12q^{26} + 24q^{29} - 96q^{39} + 12q^{41} - 12q^{44} + 150q^{49} + 150q^{51} + 36q^{54} + 48q^{56} - 6q^{59} + 84q^{61} + 90q^{64} + 126q^{66} + 48q^{69} - 36q^{74} + 12q^{76} - 96q^{79} - 144q^{81} - 12q^{84} - 48q^{86} - 48q^{89} - 36q^{91} - 216q^{94} - 384q^{99} + O(q^{100}) \)

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.u.a \(12\) \(7.586\) \(\Q(\zeta_{36})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{36}-\zeta_{36}^{7})q^{2}+(-\zeta_{36}^{5}-\zeta_{36}^{9}+\cdots)q^{3}+\cdots\)
950.2.u.b \(12\) \(7.586\) \(\Q(\zeta_{36})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{36}^{11}q^{2}+(\zeta_{36}+\zeta_{36}^{3}-\zeta_{36}^{9}+\cdots)q^{3}+\cdots\)
950.2.u.c \(12\) \(7.586\) \(\Q(\zeta_{36})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{36}^{11}q^{2}+(\zeta_{36}+\zeta_{36}^{3}-\zeta_{36}^{9}+\cdots)q^{3}+\cdots\)
950.2.u.d \(12\) \(7.586\) \(\Q(\zeta_{36})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{36}^{5}q^{2}+(-\zeta_{36}+\zeta_{36}^{3}+\zeta_{36}^{11})q^{3}+\cdots\)
950.2.u.e \(24\) \(7.586\) None \(0\) \(0\) \(0\) \(0\)
950.2.u.f \(24\) \(7.586\) None \(0\) \(0\) \(0\) \(0\)
950.2.u.g \(36\) \(7.586\) None \(0\) \(0\) \(0\) \(0\)
950.2.u.h \(48\) \(7.586\) None \(0\) \(0\) \(0\) \(0\)

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

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