Properties

Label 475.2.b
Level $475$
Weight $2$
Character orbit 475.b
Rep. character $\chi_{475}(324,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $5$
Sturm bound $100$
Trace bound $6$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 56 28 28
Cusp forms 44 28 16
Eisenstein series 12 0 12

Trace form

\( 28 q - 30 q^{4} - 4 q^{6} - 20 q^{9} + O(q^{10}) \) \( 28 q - 30 q^{4} - 4 q^{6} - 20 q^{9} + 2 q^{11} + 24 q^{14} + 34 q^{16} - 4 q^{19} - 40 q^{21} + 28 q^{24} - 8 q^{26} + 24 q^{29} - 4 q^{31} - 20 q^{34} + 26 q^{36} + 20 q^{39} + 20 q^{41} + 24 q^{44} + 12 q^{46} - 22 q^{49} - 32 q^{51} + 36 q^{54} - 80 q^{56} + 44 q^{59} + 6 q^{61} - 54 q^{64} + 4 q^{66} - 40 q^{69} - 60 q^{71} - 48 q^{74} + 10 q^{76} + 16 q^{79} - 36 q^{81} + 60 q^{84} + 36 q^{86} - 4 q^{91} - 8 q^{94} - 16 q^{96} + 2 q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
475.2.b.a \(2\) \(3.793\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{3}+2q^{4}-iq^{7}-q^{9}+3q^{11}+\cdots\)
475.2.b.b \(6\) \(3.793\) 6.0.1827904.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{4}+\beta _{5})q^{2}+(\beta _{1}+\beta _{4})q^{3}+(-1+\cdots)q^{4}+\cdots\)
475.2.b.c \(6\) \(3.793\) 6.0.153664.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}-\beta _{5})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(-3+\cdots)q^{4}+\cdots\)
475.2.b.d \(6\) \(3.793\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+(\beta _{2}-\beta _{4})q^{3}+\beta _{1}q^{4}+(-1+\cdots)q^{6}+\cdots\)
475.2.b.e \(8\) \(3.793\) 8.0.2058981376.2 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}+\beta _{1}q^{3}+(-2-\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)

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

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