Properties

Label 1045.4.a
Level $1045$
Weight $4$
Character orbit 1045.a
Rep. character $\chi_{1045}(1,\cdot)$
Character field $\Q$
Dimension $180$
Newform subspaces $9$
Sturm bound $480$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1045.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(480\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1045))\).

Total New Old
Modular forms 364 180 184
Cusp forms 356 180 176
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.

\(5\)\(11\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(23\)
\(+\)\(+\)\(-\)\(-\)\(21\)
\(+\)\(-\)\(+\)\(-\)\(23\)
\(+\)\(-\)\(-\)\(+\)\(25\)
\(-\)\(+\)\(+\)\(-\)\(22\)
\(-\)\(+\)\(-\)\(+\)\(24\)
\(-\)\(-\)\(+\)\(+\)\(22\)
\(-\)\(-\)\(-\)\(-\)\(20\)
Plus space\(+\)\(94\)
Minus space\(-\)\(86\)

Trace form

\( 180 q + 720 q^{4} - 20 q^{5} - 136 q^{6} + 24 q^{8} + 1676 q^{9} + O(q^{10}) \) \( 180 q + 720 q^{4} - 20 q^{5} - 136 q^{6} + 24 q^{8} + 1676 q^{9} - 128 q^{12} - 128 q^{14} + 2824 q^{16} + 1024 q^{18} - 200 q^{20} - 64 q^{21} - 552 q^{23} - 152 q^{24} + 4500 q^{25} + 1504 q^{26} - 528 q^{27} - 56 q^{29} + 560 q^{30} - 176 q^{31} + 2152 q^{32} + 376 q^{34} - 80 q^{35} + 9192 q^{36} - 456 q^{38} + 360 q^{39} + 568 q^{41} + 1864 q^{42} - 1520 q^{43} + 616 q^{44} + 780 q^{45} - 1968 q^{46} - 2688 q^{47} + 1880 q^{48} + 7964 q^{49} - 3280 q^{51} - 3672 q^{52} - 256 q^{53} + 2304 q^{54} - 440 q^{55} + 584 q^{56} - 2648 q^{58} + 2464 q^{59} - 184 q^{61} + 1712 q^{62} + 968 q^{63} + 8672 q^{64} - 320 q^{65} - 384 q^{67} + 5248 q^{68} + 3584 q^{69} + 1960 q^{70} + 896 q^{71} + 8840 q^{72} - 768 q^{73} + 920 q^{74} - 880 q^{77} + 4808 q^{78} - 464 q^{79} - 1920 q^{80} + 8420 q^{81} + 1472 q^{82} + 2128 q^{83} + 8520 q^{84} + 1120 q^{85} - 312 q^{86} + 9640 q^{87} - 2072 q^{89} + 2448 q^{91} - 10272 q^{92} - 11664 q^{93} - 352 q^{94} + 4888 q^{96} - 1184 q^{97} - 6344 q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1045))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 11 19
1045.4.a.a $1$ $61.657$ \(\Q\) None \(-5\) \(-1\) \(-5\) \(-2\) $+$ $+$ $-$ \(q-5q^{2}-q^{3}+17q^{4}-5q^{5}+5q^{6}+\cdots\)
1045.4.a.b $20$ $61.657$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-12\) \(-21\) \(100\) \(-131\) $-$ $-$ $-$ \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{5})q^{3}+(4+\cdots)q^{4}+\cdots\)
1045.4.a.c $20$ $61.657$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-1\) \(-8\) \(-100\) \(49\) $+$ $+$ $-$ \(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(3+\beta _{2})q^{4}-5q^{5}+\cdots\)
1045.4.a.d $22$ $61.657$ None \(-4\) \(-21\) \(110\) \(-41\) $-$ $+$ $+$
1045.4.a.e $22$ $61.657$ None \(12\) \(21\) \(110\) \(93\) $-$ $-$ $+$
1045.4.a.f $23$ $61.657$ None \(-2\) \(-9\) \(-115\) \(13\) $+$ $-$ $+$
1045.4.a.g $23$ $61.657$ None \(6\) \(9\) \(-115\) \(-37\) $+$ $+$ $+$
1045.4.a.h $24$ $61.657$ None \(4\) \(21\) \(120\) \(71\) $-$ $+$ $-$
1045.4.a.i $25$ $61.657$ None \(2\) \(9\) \(-125\) \(-15\) $+$ $-$ $-$

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1045))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1045)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 2}\)