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Properties

Label 275.2.e
Level $275$
Weight $2$
Character orbit 275.e
Rep. character $\chi_{275}(32,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $32$
Newform subspaces $4$
Sturm bound $60$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 275 = 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 275.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(60\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(275, [\chi])\).

Total New Old
Modular forms 72 40 32
Cusp forms 48 32 16
Eisenstein series 24 8 16

Trace form

\( 32 q + 6 q^{3} + O(q^{10}) \) \( 32 q + 6 q^{3} - 20 q^{11} - 8 q^{12} - 12 q^{16} + 20 q^{22} - 14 q^{23} + 56 q^{26} - 6 q^{27} - 40 q^{31} + 26 q^{33} + 12 q^{36} + 2 q^{37} - 40 q^{38} + 12 q^{47} - 4 q^{48} + 16 q^{53} - 48 q^{56} + 40 q^{58} - 80 q^{66} - 38 q^{67} + 4 q^{71} - 40 q^{78} - 60 q^{81} - 40 q^{82} - 24 q^{86} + 20 q^{88} - 24 q^{91} - 48 q^{92} - 58 q^{93} + 62 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(275, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
275.2.e.a 275.e 55.e $4$ $2.196$ \(\Q(i, \sqrt{11})\) \(\Q(\sqrt{-11}) \) \(0\) \(2\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(\beta _{1}-\beta _{2})q^{3}-2\beta _{1}q^{4}+(-1+3\beta _{1}+\cdots)q^{9}+\cdots\)
275.2.e.b 275.e 55.e $4$ $2.196$ \(\Q(i, \sqrt{10})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}+3\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
275.2.e.c 275.e 55.e $8$ $2.196$ 8.0.1499238400.2 \(\Q(\sqrt{-55}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q-\beta _{2}q^{2}+(-2\beta _{4}-\beta _{6})q^{4}+\beta _{5}q^{7}+\cdots\)
275.2.e.d 275.e 55.e $16$ $2.196$ 16.0.\(\cdots\).2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{9}q^{2}+(-\beta _{3}-\beta _{10})q^{3}+(\beta _{4}-\beta _{7}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(275, [\chi])\) into lower level spaces

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