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Properties

Label 145.4.a
Level $145$
Weight $4$
Character orbit 145.a
Rep. character $\chi_{145}(1,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $5$
Sturm bound $60$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 145 = 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 145.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(60\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(145))\).

Total New Old
Modular forms 48 28 20
Cusp forms 44 28 16
Eisenstein series 4 0 4

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

\(5\)\(29\)FrickeDim
\(+\)\(+\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(6\)
\(-\)\(+\)\(-\)\(6\)
\(-\)\(-\)\(+\)\(8\)
Plus space\(+\)\(16\)
Minus space\(-\)\(12\)

Trace form

\( 28 q + 4 q^{2} - 4 q^{3} + 124 q^{4} - 52 q^{6} - 40 q^{7} + 48 q^{8} + 312 q^{9} + O(q^{10}) \) \( 28 q + 4 q^{2} - 4 q^{3} + 124 q^{4} - 52 q^{6} - 40 q^{7} + 48 q^{8} + 312 q^{9} - 40 q^{10} - 32 q^{11} + 124 q^{12} + 24 q^{13} + 196 q^{14} + 60 q^{15} + 468 q^{16} - 124 q^{17} + 8 q^{18} - 240 q^{19} - 40 q^{20} - 184 q^{21} + 324 q^{22} - 104 q^{23} - 756 q^{24} + 700 q^{25} - 224 q^{26} - 400 q^{27} - 316 q^{28} + 80 q^{30} - 288 q^{31} + 88 q^{32} - 488 q^{33} - 236 q^{34} - 260 q^{35} + 3192 q^{36} - 804 q^{37} + 1268 q^{38} - 32 q^{39} + 880 q^{41} - 2296 q^{42} - 652 q^{43} - 1532 q^{44} + 160 q^{45} - 852 q^{46} + 1524 q^{47} + 696 q^{48} + 2496 q^{49} + 100 q^{50} + 1016 q^{51} - 1888 q^{52} - 1640 q^{53} - 3248 q^{54} + 680 q^{55} + 948 q^{56} - 2448 q^{57} + 116 q^{58} + 428 q^{59} + 800 q^{60} + 232 q^{61} + 164 q^{62} - 1584 q^{63} + 1100 q^{64} - 260 q^{65} - 2824 q^{66} - 2840 q^{67} - 48 q^{68} + 3136 q^{69} - 960 q^{70} + 456 q^{71} + 7076 q^{72} + 1836 q^{73} + 3040 q^{74} - 100 q^{75} - 5380 q^{76} + 5088 q^{77} + 1440 q^{78} - 3240 q^{79} - 2640 q^{80} - 1076 q^{81} + 2560 q^{82} - 3944 q^{83} - 1400 q^{84} + 100 q^{85} - 44 q^{86} + 1044 q^{87} + 3164 q^{88} - 2768 q^{89} - 1260 q^{90} - 1824 q^{91} - 3788 q^{92} - 2872 q^{93} + 4008 q^{94} + 440 q^{95} - 12772 q^{96} - 796 q^{97} + 2248 q^{98} + 7616 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(145))\) 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 29
145.4.a.a 145.a 1.a $1$ $8.555$ \(\Q\) None 145.4.a.a \(1\) \(-8\) \(-5\) \(-14\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-8q^{3}-7q^{4}-5q^{5}-8q^{6}+\cdots\)
145.4.a.b 145.a 1.a $6$ $8.555$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 145.4.a.b \(-7\) \(-13\) \(30\) \(-79\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}+(-2+\beta _{1}+\beta _{4})q^{3}+\cdots\)
145.4.a.c 145.a 1.a $6$ $8.555$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 145.4.a.c \(-1\) \(-1\) \(-30\) \(3\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-\beta _{3}-\beta _{4})q^{3}+(4+2\beta _{1}+\cdots)q^{4}+\cdots\)
145.4.a.d 145.a 1.a $7$ $8.555$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 145.4.a.d \(6\) \(1\) \(-35\) \(17\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{4})q^{2}-\beta _{3}q^{3}+(8-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
145.4.a.e 145.a 1.a $8$ $8.555$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 145.4.a.e \(5\) \(17\) \(40\) \(33\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(2-\beta _{3})q^{3}+(5+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(145))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(145)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 2}\)