Properties

Label 950.2.bb
Level $950$
Weight $2$
Character orbit 950.bb
Rep. character $\chi_{950}(143,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $360$
Newform subspaces $5$
Sturm bound $300$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.bb (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{36})\)
Newform subspaces: \( 5 \)
Sturm bound: \(300\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 1944 360 1584
Cusp forms 1656 360 1296
Eisenstein series 288 0 288

Trace form

\( 360 q + 12 q^{7} + O(q^{10}) \) \( 360 q + 12 q^{7} - 36 q^{17} - 48 q^{21} - 24 q^{22} + 24 q^{26} + 96 q^{33} + 24 q^{41} + 72 q^{43} + 24 q^{47} + 132 q^{51} - 36 q^{53} - 84 q^{57} + 24 q^{61} + 24 q^{62} - 36 q^{63} - 132 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} - 24 q^{76} - 96 q^{78} - 288 q^{81} - 48 q^{82} - 24 q^{83} - 96 q^{86} - 72 q^{87} - 24 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98} + O(q^{100}) \)

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.bb.a 950.bb 95.r $24$ $7.586$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{36}]$
950.2.bb.b 950.bb 95.r $48$ $7.586$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{36}]$
950.2.bb.c 950.bb 95.r $72$ $7.586$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{36}]$
950.2.bb.d 950.bb 95.r $96$ $7.586$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{36}]$
950.2.bb.e 950.bb 95.r $120$ $7.586$ None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{36}]$

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

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