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Properties

Label 230.4.a
Level $230$
Weight $4$
Character orbit 230.a
Rep. character $\chi_{230}(1,\cdot)$
Character field $\Q$
Dimension $22$
Newform subspaces $10$
Sturm bound $144$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 230.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(144\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(230))\).

Total New Old
Modular forms 112 22 90
Cusp forms 104 22 82
Eisenstein series 8 0 8

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

\(2\)\(5\)\(23\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(1\)
Plus space\(+\)\(16\)
Minus space\(-\)\(6\)

Trace form

\( 22 q - 4 q^{2} + 16 q^{3} + 88 q^{4} + 40 q^{6} + 8 q^{7} - 16 q^{8} + 114 q^{9} + 84 q^{11} + 64 q^{12} + 148 q^{13} - 80 q^{14} + 80 q^{15} + 352 q^{16} + 68 q^{17} + 76 q^{18} + 212 q^{19} + 392 q^{21}+ \cdots - 2548 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(230))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 23
230.4.a.a 230.a 1.a $1$ $13.570$ \(\Q\) None 230.4.a.a \(-2\) \(-5\) \(-5\) \(12\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-5q^{3}+4q^{4}-5q^{5}+10q^{6}+\cdots\)
230.4.a.b 230.a 1.a $1$ $13.570$ \(\Q\) None 230.4.a.b \(-2\) \(4\) \(-5\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
230.4.a.c 230.a 1.a $1$ $13.570$ \(\Q\) None 230.4.a.c \(-2\) \(7\) \(5\) \(20\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+7q^{3}+4q^{4}+5q^{5}-14q^{6}+\cdots\)
230.4.a.d 230.a 1.a $1$ $13.570$ \(\Q\) None 230.4.a.d \(2\) \(-1\) \(5\) \(-32\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+4q^{4}+5q^{5}-2q^{6}+\cdots\)
230.4.a.e 230.a 1.a $1$ $13.570$ \(\Q\) None 230.4.a.e \(2\) \(1\) \(-5\) \(-18\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+4q^{4}-5q^{5}+2q^{6}+\cdots\)
230.4.a.f 230.a 1.a $2$ $13.570$ \(\Q(\sqrt{73}) \) None 230.4.a.f \(-4\) \(-3\) \(10\) \(-17\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-1-\beta )q^{3}+4q^{4}+5q^{5}+\cdots\)
230.4.a.g 230.a 1.a $3$ $13.570$ 3.3.318165.1 None 230.4.a.g \(-6\) \(-1\) \(15\) \(7\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+5q^{5}+2\beta _{1}q^{6}+\cdots\)
230.4.a.h 230.a 1.a $4$ $13.570$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 230.4.a.h \(-8\) \(-4\) \(-20\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots\)
230.4.a.i 230.a 1.a $4$ $13.570$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 230.4.a.i \(8\) \(4\) \(-20\) \(26\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots\)
230.4.a.j 230.a 1.a $4$ $13.570$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 230.4.a.j \(8\) \(14\) \(20\) \(8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(4-\beta _{1})q^{3}+4q^{4}+5q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(230))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(230)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 2}\)