Properties

Label 275.4.b
Level $275$
Weight $4$
Character orbit 275.b
Rep. character $\chi_{275}(199,\cdot)$
Character field $\Q$
Dimension $44$
Newform subspaces $7$
Sturm bound $120$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 275 = 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 275.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(120\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(275, [\chi])\).

Total New Old
Modular forms 96 44 52
Cusp forms 84 44 40
Eisenstein series 12 0 12

Trace form

\( 44q - 192q^{4} - 8q^{6} - 336q^{9} + O(q^{10}) \) \( 44q - 192q^{4} - 8q^{6} - 336q^{9} - 44q^{11} + 52q^{14} + 592q^{16} + 24q^{19} + 64q^{21} + 428q^{24} - 568q^{26} - 320q^{29} - 688q^{31} - 104q^{34} + 1344q^{36} - 1752q^{39} + 680q^{41} + 1056q^{44} - 912q^{46} - 2588q^{49} - 800q^{51} + 3076q^{54} - 3588q^{56} + 124q^{59} + 4600q^{61} - 964q^{64} - 528q^{66} + 6716q^{69} - 184q^{71} - 9180q^{74} - 6364q^{76} + 2864q^{79} + 5116q^{81} - 5684q^{84} + 6172q^{86} - 3136q^{89} - 2072q^{91} + 6952q^{94} + 2592q^{96} + 968q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(275, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
275.4.b.a \(2\) \(16.226\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+3iq^{3}+7q^{4}-3q^{6}-9iq^{7}+\cdots\)
275.4.b.b \(4\) \(16.226\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+2\beta _{2})q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(-5+\cdots)q^{4}+\cdots\)
275.4.b.c \(4\) \(16.226\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}-4\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
275.4.b.d \(6\) \(16.226\) 6.0.5161984.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{3}+\beta _{4}-\beta _{5})q^{2}+(-\beta _{3}-3\beta _{4}+\cdots)q^{3}+\cdots\)
275.4.b.e \(8\) \(16.226\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{3}-\beta _{4})q^{3}+(-5+\beta _{2}+\cdots)q^{4}+\cdots\)
275.4.b.f \(10\) \(16.226\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{8})q^{3}+(-8+\beta _{2}+\cdots)q^{4}+\cdots\)
275.4.b.g \(10\) \(16.226\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(-2+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(275, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(275, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)