Properties

Label 230.6.a
Level $230$
Weight $6$
Character orbit 230.a
Rep. character $\chi_{230}(1,\cdot)$
Character field $\Q$
Dimension $34$
Newform subspaces $9$
Sturm bound $216$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 230.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(216\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(230))\).

Total New Old
Modular forms 184 34 150
Cusp forms 176 34 142
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.
\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(5\)
\(+\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(6\)
\(-\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(6\)
Plus space\(+\)\(12\)
Minus space\(-\)\(22\)

Trace form

\( 34q + 8q^{2} - 8q^{3} + 544q^{4} + 16q^{6} + 624q^{7} + 128q^{8} + 2502q^{9} + O(q^{10}) \) \( 34q + 8q^{2} - 8q^{3} + 544q^{4} + 16q^{6} + 624q^{7} + 128q^{8} + 2502q^{9} + 156q^{11} - 128q^{12} + 580q^{13} + 352q^{14} - 2200q^{15} + 8704q^{16} - 3172q^{17} + 5800q^{18} + 4428q^{19} + 1568q^{21} - 8560q^{22} + 256q^{24} + 21250q^{25} + 11488q^{27} + 9984q^{28} + 812q^{29} + 20244q^{31} + 2048q^{32} + 12056q^{33} - 15312q^{34} + 1800q^{35} + 40032q^{36} + 39232q^{37} + 23408q^{38} + 36232q^{39} - 1112q^{41} - 55308q^{43} + 2496q^{44} + 27576q^{47} - 2048q^{48} + 133894q^{49} + 5000q^{50} + 18120q^{51} + 9280q^{52} - 11792q^{53} + 6208q^{54} + 5632q^{56} - 21472q^{57} + 13456q^{58} - 41904q^{59} - 35200q^{60} + 33624q^{61} + 116928q^{62} + 286712q^{63} + 139264q^{64} + 87800q^{65} + 106144q^{66} - 97492q^{67} - 50752q^{68} + 19600q^{70} - 106420q^{71} + 92800q^{72} - 7076q^{73} + 54016q^{74} - 5000q^{75} + 70848q^{76} + 194632q^{77} + 60448q^{78} + 457704q^{79} + 553522q^{81} + 200528q^{82} + 284428q^{83} + 25088q^{84} + 66200q^{85} + 12112q^{86} + 55784q^{87} - 136960q^{88} + 75100q^{89} + 27968q^{91} + 125912q^{93} + 132832q^{94} - 75800q^{95} + 4096q^{96} + 178892q^{97} - 449592q^{98} + 776372q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(230))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 23
230.6.a.a \(1\) \(36.888\) \(\Q\) None \(-4\) \(8\) \(-25\) \(199\) \(+\) \(+\) \(+\) \(q-4q^{2}+8q^{3}+2^{4}q^{4}-5^{2}q^{5}-2^{5}q^{6}+\cdots\)
230.6.a.b \(2\) \(36.888\) \(\Q(\sqrt{2}) \) None \(-8\) \(6\) \(-50\) \(-164\) \(+\) \(+\) \(+\) \(q-4q^{2}+(3+6\beta )q^{3}+2^{4}q^{4}-5^{2}q^{5}+\cdots\)
230.6.a.c \(3\) \(36.888\) 3.3.27980.1 None \(-12\) \(-26\) \(75\) \(1\) \(+\) \(-\) \(-\) \(q-4q^{2}+(-9+\beta _{2})q^{3}+2^{4}q^{4}+5^{2}q^{5}+\cdots\)
230.6.a.d \(3\) \(36.888\) 3.3.27980.1 None \(12\) \(-34\) \(75\) \(-121\) \(-\) \(-\) \(+\) \(q+4q^{2}+(-11-\beta _{2})q^{3}+2^{4}q^{4}+5^{2}q^{5}+\cdots\)
230.6.a.e \(3\) \(36.888\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(12\) \(6\) \(-75\) \(5\) \(-\) \(+\) \(-\) \(q+4q^{2}+(2-\beta _{1})q^{3}+2^{4}q^{4}-5^{2}q^{5}+\cdots\)
230.6.a.f \(5\) \(36.888\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-20\) \(1\) \(125\) \(102\) \(+\) \(-\) \(+\) \(q-4q^{2}+\beta _{1}q^{3}+2^{4}q^{4}+5^{2}q^{5}-4\beta _{1}q^{6}+\cdots\)
230.6.a.g \(5\) \(36.888\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-20\) \(5\) \(-125\) \(130\) \(+\) \(+\) \(-\) \(q-4q^{2}+(1+\beta _{1})q^{3}+2^{4}q^{4}-5^{2}q^{5}+\cdots\)
230.6.a.h \(6\) \(36.888\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(24\) \(11\) \(150\) \(366\) \(-\) \(-\) \(-\) \(q+4q^{2}+(2-\beta _{1})q^{3}+2^{4}q^{4}+5^{2}q^{5}+\cdots\)
230.6.a.i \(6\) \(36.888\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(24\) \(15\) \(-150\) \(106\) \(-\) \(+\) \(+\) \(q+4q^{2}+(2+\beta _{1})q^{3}+2^{4}q^{4}-5^{2}q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(230))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(230)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 2}\)