Properties

Label 475.2.j
Level $475$
Weight $2$
Character orbit 475.j
Rep. character $\chi_{475}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $56$
Newform subspaces $4$
Sturm bound $100$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(100\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(475, [\chi])\).

Total New Old
Modular forms 112 64 48
Cusp forms 88 56 32
Eisenstein series 24 8 16

Trace form

\( 56 q + 24 q^{4} + 10 q^{6} + 26 q^{9} + O(q^{10}) \) \( 56 q + 24 q^{4} + 10 q^{6} + 26 q^{9} - 20 q^{11} - 16 q^{16} + 16 q^{19} + 10 q^{21} + 26 q^{24} + 68 q^{26} - 6 q^{29} - 44 q^{31} - 22 q^{34} - 14 q^{36} - 56 q^{39} + 10 q^{41} - 30 q^{44} - 96 q^{46} + 16 q^{49} + 26 q^{51} - 12 q^{54} - 88 q^{56} - 20 q^{59} - 42 q^{61} - 72 q^{64} - 64 q^{66} + 4 q^{69} - 12 q^{71} + 24 q^{74} + 140 q^{76} + 2 q^{79} + 36 q^{81} + 108 q^{84} + 30 q^{86} - 12 q^{89} + 46 q^{91} + 8 q^{94} + 100 q^{96} + 16 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(475, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
475.2.j.a 475.j 95.i $4$ $3.793$ \(\Q(\zeta_{12})\) None 95.2.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{3}-2\zeta_{12}^{2}q^{4}+2\zeta_{12}^{3}q^{7}+\cdots\)
475.2.j.b 475.j 95.i $12$ $3.793$ 12.0.\(\cdots\).1 None 95.2.e.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}-\beta _{11}q^{3}+(2-\beta _{2}+3\beta _{3}+\cdots)q^{4}+\cdots\)
475.2.j.c 475.j 95.i $16$ $3.793$ 16.0.\(\cdots\).1 None 95.2.e.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{14}q^{2}+(\beta _{7}+\beta _{13})q^{3}+(-\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots\)
475.2.j.d 475.j 95.i $24$ $3.793$ None 475.2.e.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(475, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(475, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)