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Properties

Label 275.2.z
Level $275$
Weight $2$
Character orbit 275.z
Rep. character $\chi_{275}(49,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $64$
Newform subspaces $3$
Sturm bound $60$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 275 = 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 275.z (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 3 \)
Sturm bound: \(60\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 144 80 64
Cusp forms 96 64 32
Eisenstein series 48 16 32

Trace form

\( 64 q + 20 q^{4} + 6 q^{6} + 4 q^{9} - 14 q^{11} - 6 q^{14} - 40 q^{16} - 2 q^{19} - 44 q^{21} + 10 q^{24} - 76 q^{26} + 2 q^{29} - 28 q^{31} - 8 q^{34} + 18 q^{36} - 66 q^{39} + 58 q^{41} + 82 q^{44} + 4 q^{46}+ \cdots + 52 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
275.2.z.a 275.z 55.j $16$ $2.196$ 16.0.\(\cdots\).1 None 55.2.g.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q-\beta _{4}q^{2}+(-\beta _{1}-\beta _{11}-\beta _{13}+\beta _{15})q^{3}+\cdots\)
275.2.z.b 275.z 55.j $16$ $2.196$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 55.2.g.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\beta _{6}+\beta _{12}-\beta _{15})q^{2}+(\beta _{14}-\beta _{15})q^{3}+\cdots\)
275.2.z.c 275.z 55.j $32$ $2.196$ None 275.2.h.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$

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

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