Properties

Label 375.2.b
Level $375$
Weight $2$
Character orbit 375.b
Rep. character $\chi_{375}(124,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $3$
Sturm bound $100$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 375 = 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 375.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(100\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(375, [\chi])\).

Total New Old
Modular forms 60 16 44
Cusp forms 40 16 24
Eisenstein series 20 0 20

Trace form

\( 16 q - 18 q^{4} + 2 q^{6} - 16 q^{9} + O(q^{10}) \) \( 16 q - 18 q^{4} + 2 q^{6} - 16 q^{9} + 4 q^{11} - 12 q^{14} + 30 q^{16} + 8 q^{19} - 16 q^{21} - 6 q^{24} + 12 q^{26} - 4 q^{29} - 4 q^{31} - 16 q^{34} + 18 q^{36} + 12 q^{39} + 16 q^{41} + 76 q^{44} - 84 q^{46} - 20 q^{49} + 8 q^{51} - 2 q^{54} - 60 q^{56} - 28 q^{59} + 38 q^{64} + 16 q^{66} - 12 q^{69} + 32 q^{71} + 68 q^{74} - 12 q^{76} + 40 q^{79} + 16 q^{81} + 52 q^{84} - 56 q^{86} - 32 q^{89} - 44 q^{91} + 2 q^{94} - 36 q^{96} - 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(375, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
375.2.b.a 375.b 5.b $4$ $2.994$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{3})q^{2}-\beta _{3}q^{3}+3\beta _{2}q^{4}+(-1+\cdots)q^{6}+\cdots\)
375.2.b.b 375.b 5.b $4$ $2.994$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-\beta _{2}q^{6}+\cdots\)
375.2.b.c 375.b 5.b $8$ $2.994$ 8.0.1632160000.5 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{4}+\beta _{7})q^{2}-\beta _{4}q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(375, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(375, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 2}\)