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Properties

Label 572.2.e
Level $572$
Weight $2$
Character orbit 572.e
Rep. character $\chi_{572}(131,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $2$
Sturm bound $168$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 572.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 44 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(168\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(572, [\chi])\).

Total New Old
Modular forms 88 72 16
Cusp forms 80 72 8
Eisenstein series 8 0 8

Trace form

\( 72 q + 4 q^{4} - 80 q^{9} + O(q^{10}) \) \( 72 q + 4 q^{4} - 80 q^{9} - 8 q^{12} - 4 q^{14} + 12 q^{16} - 16 q^{22} + 88 q^{25} - 16 q^{33} - 30 q^{36} - 32 q^{37} - 38 q^{38} + 54 q^{42} + 4 q^{44} - 24 q^{45} + 34 q^{48} + 56 q^{49} - 94 q^{56} + 12 q^{58} + 4 q^{60} - 20 q^{64} - 30 q^{66} - 24 q^{69} - 92 q^{70} + 44 q^{77} - 10 q^{78} - 8 q^{80} + 136 q^{81} - 76 q^{82} + 80 q^{86} + 36 q^{88} + 8 q^{89} + 94 q^{92} + 8 q^{93} - 56 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(572, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
572.2.e.a 572.e 44.c $8$ $4.567$ 8.0.342102016.5 None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(-\beta _{3}-\beta _{5}+\beta _{7})q^{4}+(-2+\cdots)q^{5}+\cdots\)
572.2.e.b 572.e 44.c $64$ $4.567$ None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(572, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(572, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 2}\)