Properties

Label 588.2.ba
Level $588$
Weight $2$
Character orbit 588.ba
Rep. character $\chi_{588}(103,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $672$
Newform subspaces $2$
Sturm bound $224$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 588.ba (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 196 \)
Character field: \(\Q(\zeta_{42})\)
Newform subspaces: \( 2 \)
Sturm bound: \(224\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(588, [\chi])\).

Total New Old
Modular forms 1392 672 720
Cusp forms 1296 672 624
Eisenstein series 96 0 96

Trace form

\( 672 q - 12 q^{8} + 56 q^{9} + O(q^{10}) \) \( 672 q - 12 q^{8} + 56 q^{9} + 18 q^{10} + 22 q^{14} + 8 q^{16} + 8 q^{21} + 12 q^{22} + 24 q^{24} - 52 q^{25} - 30 q^{26} + 36 q^{28} - 8 q^{30} - 10 q^{32} + 12 q^{33} + 112 q^{34} + 32 q^{37} - 18 q^{38} - 26 q^{40} - 16 q^{42} - 64 q^{44} - 8 q^{49} - 228 q^{50} - 36 q^{52} - 8 q^{53} - 40 q^{56} - 24 q^{57} - 6 q^{58} + 10 q^{60} + 4 q^{61} - 8 q^{65} + 36 q^{66} + 36 q^{68} - 108 q^{70} + 48 q^{72} + 36 q^{73} + 22 q^{74} + 42 q^{76} - 16 q^{77} - 12 q^{78} - 54 q^{80} + 56 q^{81} - 186 q^{82} + 40 q^{84} + 48 q^{85} - 188 q^{86} - 284 q^{88} + 28 q^{92} - 4 q^{93} - 336 q^{94} - 30 q^{96} - 278 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(588, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
588.2.ba.a $336$ $4.695$ None \(0\) \(-28\) \(0\) \(2\)
588.2.ba.b $336$ $4.695$ None \(0\) \(28\) \(0\) \(-2\)

Decomposition of \(S_{2}^{\mathrm{old}}(588, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(588, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)