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Properties

Label 252.3.g
Level $252$
Weight $3$
Character orbit 252.g
Rep. character $\chi_{252}(127,\cdot)$
Character field $\Q$
Dimension $30$
Newform subspaces $3$
Sturm bound $144$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 252.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(144\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(252, [\chi])\).

Total New Old
Modular forms 104 30 74
Cusp forms 88 30 58
Eisenstein series 16 0 16

Trace form

\( 30 q - q^{2} - 7 q^{4} - 4 q^{5} + 23 q^{8} + O(q^{10}) \) \( 30 q - q^{2} - 7 q^{4} - 4 q^{5} + 23 q^{8} + 28 q^{10} + 12 q^{13} + 7 q^{14} - 11 q^{16} + 44 q^{17} + 52 q^{20} - 40 q^{22} + 90 q^{25} - 44 q^{26} - 7 q^{28} - 36 q^{29} - 41 q^{32} - 22 q^{34} + 44 q^{37} + 62 q^{38} + 176 q^{40} + 220 q^{41} - 124 q^{44} + 156 q^{46} - 210 q^{49} + 185 q^{50} - 76 q^{52} - 196 q^{53} - 49 q^{56} - 314 q^{58} + 44 q^{61} - 212 q^{62} - 247 q^{64} - 40 q^{65} - 250 q^{68} - 84 q^{70} - 132 q^{73} - 254 q^{74} - 6 q^{76} + 112 q^{77} + 252 q^{80} + 386 q^{82} + 328 q^{85} + 4 q^{86} - 56 q^{88} + 204 q^{89} - 128 q^{92} - 300 q^{94} + 252 q^{97} + 7 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
252.3.g.a 252.g 4.b $6$ $6.867$ 6.0.1539727.2 None \(1\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{4})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
252.3.g.b 252.g 4.b $12$ $6.867$ 12.0.\(\cdots\).1 None \(-2\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-\beta _{5}q^{4}+(-\beta _{3}+\beta _{8})q^{5}+\cdots\)
252.3.g.c 252.g 4.b $12$ $6.867$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(-1-\beta _{6})q^{4}+(-\beta _{2}+\beta _{7}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)