Properties

Label 275.4.a
Level $275$
Weight $4$
Character orbit 275.a
Rep. character $\chi_{275}(1,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $11$
Sturm bound $120$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 275 = 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 275.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(120\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(275))\).

Total New Old
Modular forms 96 48 48
Cusp forms 84 48 36
Eisenstein series 12 0 12

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(5\)\(11\)FrickeDim
\(+\)\(+\)\(+\)\(12\)
\(+\)\(-\)\(-\)\(10\)
\(-\)\(+\)\(-\)\(11\)
\(-\)\(-\)\(+\)\(15\)
Plus space\(+\)\(27\)
Minus space\(-\)\(21\)

Trace form

\( 48 q - 2 q^{2} + 2 q^{3} + 208 q^{4} - 34 q^{6} + 20 q^{7} + 24 q^{8} + 406 q^{9} + 22 q^{11} + 24 q^{12} - 88 q^{13} - 96 q^{14} + 808 q^{16} + 60 q^{17} + 420 q^{18} + 48 q^{19} + 44 q^{21} - 22 q^{22}+ \cdots + 924 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(275))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 11
275.4.a.a 275.a 1.a $1$ $16.226$ \(\Q\) None 55.4.a.a \(-1\) \(3\) \(0\) \(9\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}-7q^{4}-3q^{6}+9q^{7}+\cdots\)
275.4.a.b 275.a 1.a $2$ $16.226$ \(\Q(\sqrt{3}) \) None 11.4.a.a \(-2\) \(2\) \(0\) \(-20\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-4\beta )q^{3}+(-4-2\beta )q^{4}+\cdots\)
275.4.a.c 275.a 1.a $2$ $16.226$ \(\Q(\sqrt{17}) \) None 55.4.a.b \(7\) \(3\) \(0\) \(25\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(4-\beta )q^{2}+(2-\beta )q^{3}+(12-7\beta )q^{4}+\cdots\)
275.4.a.d 275.a 1.a $3$ $16.226$ 3.3.568.1 None 55.4.a.c \(-5\) \(3\) \(0\) \(15\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1}+\beta _{2})q^{2}+(2+3\beta _{2})q^{3}+\cdots\)
275.4.a.e 275.a 1.a $4$ $16.226$ 4.4.1539480.1 None 55.4.a.d \(-1\) \(-9\) \(0\) \(-9\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-2+\beta _{2})q^{3}+(5+\beta _{1}+\beta _{3})q^{4}+\cdots\)
275.4.a.f 275.a 1.a $5$ $16.226$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 275.4.a.f \(-2\) \(-12\) \(0\) \(-24\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-2-\beta _{3})q^{3}+(2+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
275.4.a.g 275.a 1.a $5$ $16.226$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 275.4.a.g \(-2\) \(0\) \(0\) \(-40\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{4})q^{3}+(8+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
275.4.a.h 275.a 1.a $5$ $16.226$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 275.4.a.g \(2\) \(0\) \(0\) \(40\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{4})q^{3}+(8+\beta _{2}+\cdots)q^{4}+\cdots\)
275.4.a.i 275.a 1.a $5$ $16.226$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 275.4.a.f \(2\) \(12\) \(0\) \(24\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{3})q^{3}+(2+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
275.4.a.j 275.a 1.a $6$ $16.226$ 6.6.2301792529.1 None 55.4.b.a \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
275.4.a.k 275.a 1.a $10$ $16.226$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 55.4.b.b \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(6+\beta _{2})q^{4}+(3-\beta _{3}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(275))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(275)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 2}\)