Properties

Label 575.4.a
Level $575$
Weight $4$
Character orbit 575.a
Rep. character $\chi_{575}(1,\cdot)$
Character field $\Q$
Dimension $105$
Newform subspaces $18$
Sturm bound $240$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 575 = 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 575.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(240\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(575))\).

Total New Old
Modular forms 186 105 81
Cusp forms 174 105 69
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.

\(5\)\(23\)FrickeDim
\(+\)\(+\)\(+\)\(29\)
\(+\)\(-\)\(-\)\(20\)
\(-\)\(+\)\(-\)\(25\)
\(-\)\(-\)\(+\)\(31\)
Plus space\(+\)\(60\)
Minus space\(-\)\(45\)

Trace form

\( 105 q - 4 q^{2} + 2 q^{3} + 424 q^{4} + 17 q^{6} + 32 q^{7} - 3 q^{8} + 965 q^{9} + O(q^{10}) \) \( 105 q - 4 q^{2} + 2 q^{3} + 424 q^{4} + 17 q^{6} + 32 q^{7} - 3 q^{8} + 965 q^{9} + 58 q^{11} + q^{12} - 114 q^{13} - 52 q^{14} + 1712 q^{16} + 202 q^{17} + 349 q^{18} - 46 q^{19} - 100 q^{21} - 616 q^{22} - 69 q^{23} + 688 q^{24} + 5 q^{26} + 278 q^{27} - 34 q^{28} - 246 q^{29} - 110 q^{31} + 552 q^{32} + 388 q^{33} - 566 q^{34} + 4531 q^{36} + 984 q^{37} - 228 q^{38} + 1146 q^{39} + 190 q^{41} + 152 q^{42} + 954 q^{43} - 934 q^{44} + 92 q^{46} - 362 q^{47} - 1029 q^{48} + 5169 q^{49} - 2520 q^{51} - 1045 q^{52} - 772 q^{53} + 479 q^{54} - 934 q^{56} + 1032 q^{57} + 127 q^{58} + 1128 q^{59} + 2244 q^{61} + 1433 q^{62} + 884 q^{63} + 9647 q^{64} - 862 q^{66} + 782 q^{67} + 4036 q^{68} + 276 q^{69} - 854 q^{71} + 4383 q^{72} - 2246 q^{73} + 1178 q^{74} - 348 q^{76} - 1248 q^{77} + 1071 q^{78} - 1280 q^{79} + 8753 q^{81} - 799 q^{82} + 634 q^{83} + 5866 q^{84} - 162 q^{86} - 3066 q^{87} - 2784 q^{88} + 2438 q^{89} - 1188 q^{91} - 552 q^{92} - 1992 q^{93} + 4069 q^{94} + 3071 q^{96} + 2098 q^{97} + 3736 q^{98} + 3726 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(575))\) 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 23
575.4.a.a 575.a 1.a $1$ $33.926$ \(\Q\) None 115.4.a.b \(-2\) \(3\) \(0\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}-4q^{4}-6q^{6}+2q^{7}+\cdots\)
575.4.a.b 575.a 1.a $1$ $33.926$ \(\Q\) None 115.4.a.a \(-1\) \(-4\) \(0\) \(32\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-4q^{3}-7q^{4}+4q^{6}+2^{5}q^{7}+\cdots\)
575.4.a.c 575.a 1.a $1$ $33.926$ \(\Q\) None 575.4.a.c \(-1\) \(6\) \(0\) \(7\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+6q^{3}-7q^{4}-6q^{6}+7q^{7}+\cdots\)
575.4.a.d 575.a 1.a $1$ $33.926$ \(\Q\) None 575.4.a.d \(-1\) \(10\) \(0\) \(-23\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+10q^{3}-7q^{4}-10q^{6}-23q^{7}+\cdots\)
575.4.a.e 575.a 1.a $1$ $33.926$ \(\Q\) None 575.4.a.d \(1\) \(-10\) \(0\) \(23\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-10q^{3}-7q^{4}-10q^{6}+23q^{7}+\cdots\)
575.4.a.f 575.a 1.a $1$ $33.926$ \(\Q\) None 575.4.a.c \(1\) \(-6\) \(0\) \(-7\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-6q^{3}-7q^{4}-6q^{6}-7q^{7}+\cdots\)
575.4.a.g 575.a 1.a $1$ $33.926$ \(\Q\) None 23.4.a.a \(2\) \(5\) \(0\) \(8\) $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+5q^{3}-4q^{4}+10q^{6}+8q^{7}+\cdots\)
575.4.a.h 575.a 1.a $2$ $33.926$ \(\Q(\sqrt{109}) \) None 115.4.a.c \(6\) \(3\) \(0\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{2}+(2-\beta )q^{3}+q^{4}+(6-3\beta )q^{6}+\cdots\)
575.4.a.i 575.a 1.a $4$ $33.926$ 4.4.334189.1 None 23.4.a.b \(-2\) \(-7\) \(0\) \(-16\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{3})q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+\cdots\)
575.4.a.j 575.a 1.a $5$ $33.926$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 115.4.a.e \(-6\) \(-4\) \(0\) \(3\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}+(-1-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots\)
575.4.a.k 575.a 1.a $5$ $33.926$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 115.4.a.d \(5\) \(6\) \(0\) \(15\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1+\beta _{2}+\beta _{3}+\beta _{4})q^{3}+\cdots\)
575.4.a.l 575.a 1.a $7$ $33.926$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 575.4.a.l \(-3\) \(-1\) \(0\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{5})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots\)
575.4.a.m 575.a 1.a $7$ $33.926$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 575.4.a.l \(3\) \(1\) \(0\) \(1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{5})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots\)
575.4.a.n 575.a 1.a $8$ $33.926$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 115.4.a.f \(-6\) \(0\) \(0\) \(-11\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-\beta _{6}q^{3}+(5+\beta _{2})q^{4}+\cdots\)
575.4.a.o 575.a 1.a $13$ $33.926$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None 575.4.a.o \(-3\) \(3\) \(0\) \(1\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(6+\beta _{2})q^{4}+(5-\beta _{1}+\cdots)q^{6}+\cdots\)
575.4.a.p 575.a 1.a $13$ $33.926$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None 575.4.a.o \(3\) \(-3\) \(0\) \(-1\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(6+\beta _{2})q^{4}+(5-\beta _{1}+\cdots)q^{6}+\cdots\)
575.4.a.q 575.a 1.a $17$ $33.926$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None 115.4.b.a \(-4\) \(-12\) \(0\) \(-72\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(4+\beta _{2})q^{4}+\cdots\)
575.4.a.r 575.a 1.a $17$ $33.926$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None 115.4.b.a \(4\) \(12\) \(0\) \(72\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(4+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(575))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(575)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 2}\)