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

\( 22 q - 4 q^{2} + 16 q^{3} + 88 q^{4} + 40 q^{6} + 8 q^{7} - 16 q^{8} + 114 q^{9} + O(q^{10}) \) \( 22 q - 4 q^{2} + 16 q^{3} + 88 q^{4} + 40 q^{6} + 8 q^{7} - 16 q^{8} + 114 q^{9} + 84 q^{11} + 64 q^{12} + 148 q^{13} - 80 q^{14} + 80 q^{15} + 352 q^{16} + 68 q^{17} + 76 q^{18} + 212 q^{19} + 392 q^{21} + 40 q^{22} + 160 q^{24} + 550 q^{25} + 832 q^{27} + 32 q^{28} + 584 q^{29} - 440 q^{31} - 64 q^{32} - 232 q^{33} + 360 q^{34} - 180 q^{35} + 456 q^{36} + 200 q^{37} + 920 q^{38} + 304 q^{39} - 308 q^{41} + 732 q^{43} + 336 q^{44} - 912 q^{47} + 256 q^{48} + 2678 q^{49} - 100 q^{50} + 1920 q^{51} + 592 q^{52} - 872 q^{53} + 928 q^{54} - 320 q^{56} + 1568 q^{57} - 232 q^{58} - 444 q^{59} + 320 q^{60} - 512 q^{61} - 288 q^{62} - 1168 q^{63} + 1408 q^{64} + 1280 q^{65} - 848 q^{66} + 1580 q^{67} + 272 q^{68} - 280 q^{70} - 280 q^{71} + 304 q^{72} - 60 q^{73} - 1664 q^{74} + 400 q^{75} + 848 q^{76} - 1712 q^{77} - 3440 q^{78} - 1344 q^{79} - 3002 q^{81} - 360 q^{82} - 3236 q^{83} + 1568 q^{84} - 1220 q^{85} - 3320 q^{86} - 3616 q^{87} + 160 q^{88} - 2924 q^{89} - 1032 q^{91} - 5632 q^{93} - 144 q^{94} + 40 q^{95} + 640 q^{96} - 36 q^{97} - 804 q^{98} - 2548 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(230))\) 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
230.4.a.a \(1\) \(13.570\) \(\Q\) None \(-2\) \(-5\) \(-5\) \(12\) \(+\) \(+\) \(-\) \(q-2q^{2}-5q^{3}+4q^{4}-5q^{5}+10q^{6}+\cdots\)
230.4.a.b \(1\) \(13.570\) \(\Q\) None \(-2\) \(4\) \(-5\) \(3\) \(+\) \(+\) \(-\) \(q-2q^{2}+4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
230.4.a.c \(1\) \(13.570\) \(\Q\) None \(-2\) \(7\) \(5\) \(20\) \(+\) \(-\) \(-\) \(q-2q^{2}+7q^{3}+4q^{4}+5q^{5}-14q^{6}+\cdots\)
230.4.a.d \(1\) \(13.570\) \(\Q\) None \(2\) \(-1\) \(5\) \(-32\) \(-\) \(-\) \(-\) \(q+2q^{2}-q^{3}+4q^{4}+5q^{5}-2q^{6}+\cdots\)
230.4.a.e \(1\) \(13.570\) \(\Q\) None \(2\) \(1\) \(-5\) \(-18\) \(-\) \(+\) \(+\) \(q+2q^{2}+q^{3}+4q^{4}-5q^{5}+2q^{6}+\cdots\)
230.4.a.f \(2\) \(13.570\) \(\Q(\sqrt{73}) \) None \(-4\) \(-3\) \(10\) \(-17\) \(+\) \(-\) \(+\) \(q-2q^{2}+(-1-\beta )q^{3}+4q^{4}+5q^{5}+\cdots\)
230.4.a.g \(3\) \(13.570\) 3.3.318165.1 None \(-6\) \(-1\) \(15\) \(7\) \(+\) \(-\) \(-\) \(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+5q^{5}+2\beta _{1}q^{6}+\cdots\)
230.4.a.h \(4\) \(13.570\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-8\) \(-4\) \(-20\) \(-1\) \(+\) \(+\) \(+\) \(q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots\)
230.4.a.i \(4\) \(13.570\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(8\) \(4\) \(-20\) \(26\) \(-\) \(+\) \(-\) \(q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots\)
230.4.a.j \(4\) \(13.570\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(8\) \(14\) \(20\) \(8\) \(-\) \(-\) \(+\) \(q+2q^{2}+(4-\beta _{1})q^{3}+4q^{4}+5q^{5}+\cdots\)

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

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