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Properties

Label 1175.4.c
Level $1175$
Weight $4$
Character orbit 1175.c
Rep. character $\chi_{1175}(424,\cdot)$
Character field $\Q$
Dimension $206$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1175 = 5^{2} \cdot 47 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1175.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1175, [\chi])\).

Total New Old
Modular forms 366 206 160
Cusp forms 354 206 148
Eisenstein series 12 0 12

Trace form

\( 206 q - 816 q^{4} - 24 q^{6} - 1818 q^{9} + O(q^{10}) \) \( 206 q - 816 q^{4} - 24 q^{6} - 1818 q^{9} - 96 q^{14} + 3312 q^{16} + 24 q^{19} - 168 q^{21} - 476 q^{24} + 84 q^{26} - 520 q^{29} + 800 q^{31} + 632 q^{34} + 6056 q^{36} - 1472 q^{39} + 1504 q^{41} + 2932 q^{44} - 420 q^{46} - 11726 q^{49} - 676 q^{51} + 2004 q^{54} + 1060 q^{56} + 276 q^{59} + 2100 q^{61} - 13388 q^{64} - 2844 q^{66} - 688 q^{69} - 1348 q^{71} - 3668 q^{74} + 2596 q^{76} + 3460 q^{79} + 13646 q^{81} - 6400 q^{84} + 7444 q^{86} - 1688 q^{89} - 2584 q^{91} + 752 q^{94} + 1704 q^{96} - 4148 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1175, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1175, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1175, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)